8  6, 8  6 6 6 | HP 35s Scientific

Examples:

Here are some examples of trigonometry and arithmetic with complex numbers:

Evaluate sin (2i3)

Keys:

8() 6

Evaluate the expression

Display:Description:

Sets display format.

 Result is 9.1545 i –4.1689.

z 1 ⎟ (z2 + z3),

where z1 = 23 i 13, z2 = –2i1 z3 = 4 i– 3 Perform the calculation as

Keys:

8() 6

6

6



Display:		Description:
		Sets display format
		ENTER z1
	
		ENTER z2
	
		(z2 + z3). Result is 2 i -2.
	
		z 1 ⎟(z2 + z3). Result is 2.5
		i 9.

Evaluate (4 i –2/5) × (3 i –2/3).

Keys:	Display:	Description:
8( )		Sets display format
6  		Enters 4i-2/5
	 

9-4Operations with Complex Numbers

Image 146

HP 35s Scientific manual 8  6, 8  6 6 6, Display Description, 4Operations with Complex Numbers

Contents

HP 35s scientific calculator Users guide Printing History Contents Storing Data into Variables Viewing a Variable ContentsRPN The Automatic Memory Stack Trigonometry Entering π Real-Number FunctionsQuotient and Remainder of Division Hyperbolic Functions Fractions Entering and Evaluating Equations Operations with Complex Numbers Solving EquationsIntegrating Equations Vector Arithmetic 10-1 10-7 Base Conversions and Arithmetic and Logic 11-1Statistical Operations 12-1 Creating Vectors from Variables or Registers 10-8 Part 2. Programming Simple Programming 13-1 Programming Techniques 14-1 Solving and Integrating Programs 15-1 Support, Batteries, and ServicePart 3. Appendixes and Reference Statistics Programs 16-1 More about Solving User Memory and the StackALG Summary Messages Operation Index Round-Off ErrorMore about Integration How the Integral Is Evaluated Contents Part Page Important Preliminaries Adjusting Display ContrastGetting Started Turning the Calculator On and Off 2Getting Started Highlights of the Keyboard and DisplayShifted Keys Function Key Alpha KeysCursor Keys Left-shifted function Right-shifted Letter for alphabetic Keys for Clearing  Clear or CancelBackspacing and Clearing 4Getting Started Key Description Clear menu       HP 35s Menus Chapter Name Using Menusˆ ˆ    6Getting Started Programming Instructions Other functions  Exiting Menusor  8 Keys Display RPN and ALG Modes KeysDisplay RPN mode ALG mode 10Getting Started Undo key Annunciators Display and AnnunciatorsFirst Line Second Line 12Getting Started HP 35s Annunciators Meaning Chapter EQN 14Getting Started Exponents of Ten Keying in NumbersMaking Numbers Negative 16Getting Started z  Understanding Entry CursorRange of Numbers and Overflow  18Getting Started Performing Arithmetic CalculationsSingle Argument or Unary Operations Key RPN,RPN Program ALG, Equation, ALG Program Two Argument or Binary Operations   Õ Controlling the Display Format Key RPN, RPN Program ALG, Equation, ALG Program 22Getting Started Periods and Commas in Numbers   8 Complex number display format  ,  , 8 24Getting Started 8× SHOWing Full 12-Digit Precision8    26Getting Started FractionsEntering Fractions  É Messages  28Getting Started Calculator MemoryChecking Available Memory Clearing All of Memory 30Getting Started RPN The Automatic Memory Stack RPN The Automatic Memory StackWhat the Stack Is 2RPN The Automatic Memory Stack Reviewing the Stack X and Y-Registers are in the DisplayClearing the X-Register 4RPN The Automatic Memory Stack Exchanging the X- and Y-Registers in the StackPress  Arithmetic How the Stack Does It How Enter Works 6RPN The Automatic Memory Stack How to Clear the Stack Filling the stack with a constant Last X Register 8RPN The Automatic Memory Stack Correcting Mistakes with Last  Reusing Numbers with Last Ù     Chain Calculations in RPN ModeWork from the Parentheses Out      ExercisesOrder of Calculation       More Exercises       18RPN The Automatic Memory Stack Storing Data into Variables AKeys DisplayDescription Press letter-key  Storing and Recalling Numbers2Storing Data into Variables Press letter-key    AG  VAR catalog Using the MEM CatalogViewing a Variable 4Storing Data into Variables C D E 6Storing Data into Variables Arithmetic with Stored VariablesStorage Arithmetic Storage arithmetic uses , , , or  Recall Arithmetic D Exchanging x with Any Variable D E A Variables I and J 10Storing Data into Variables Exponential and Logarithmic Functions Real-Number Functions   Power FunctionsQuotient and Remainder of Division   Trigonometry Entering π Option Description Annunciator Setting the Angular ModeTrigonometric Functions 4Real-Number Functions   Hyperbolic Functions Percentage Functions     8Real-Number Functions Physics ConstantsConst Menu Items Description Value Items Description Value 10Real-Number Functions Conversion FunctionsRectangular/Polar Conversions 30o 12Real-Number Functions 86  Time ConversionsAngle Conversions Unit Conversions Gamma Probability FunctionsFactorial Probability 16Real-Number Functions  Fractional part Parts of NumbersInteger part Absolute value 18Real-Number Functions To calculatePressDisplay   FractionsEntering Fractions 2Fractions Fractions in the DisplayDisplay Rules Accuracy Indicators Entered Value Internal Value Displayed Fraction 4Fractions Setting the Maximum DenominatorChanging the Fraction Display  Choosing a Fraction Format 6Fractions   j To Get This Fraction Format Change These Flags Rounding Fractions Examples of Fraction Displays Fractions in Equations Fractions in Programs 10Fractions Entering and Evaluating Equations Entering and Evaluating EquationsHow You Can Use Equations = .25 π d2 l Value      D 2Entering and Evaluating Equations Summary of Equation Operations Key Operation 4Entering and Evaluating Equations Entering Equations into the Equation ListVariables in Equations Numbers in Equations Functions in Equations   Displaying and Selecting EquationsParentheses in Equations  Ö  Editing and Clearing Equations 8Entering and Evaluating Equations Types of Equations Evaluating Equations 10Entering and Evaluating Equations Using Enter for Evaluation Type of Equation Result for  Result for  12Entering and Evaluating Equations Using XEQ for Evaluation       Responding to Equation Prompts 14Entering and Evaluating Equations Syntax of EquationsOperator Precedence Order Operation Example Equations Meaning Σxy Equation Functions16Entering and Evaluating Equations RPN Operation Equation function Perimeter = a + b + h sin1θ + sin1φ 18Entering and Evaluating Equations Area =  Õ Syntax ErrorsVerifying Equations 20Entering and Evaluating Equations Solving Equations Solving EquationsSolving an Equation Markup ⋅ Cost = Price 2Solving Equations = v0 t + 1/2 g t G    P       P    Solving built-in Equation 6Solving Equations  Understanding and Controlling SolveVerifying the Result 8Solving Equations Interrupting a Solve CalculationChoosing Initial Guesses for Solve Solving Equations Type in the equation 10Solving Equations= 40 H ⋅ 20 H ⋅ 4 ⋅ H Equation H  value 4H   For More Information 12Solving Equations Integrating Equations Integrating Equations Integrating Equations FN 2Integrating Equations J0 x = π 0 cosx sin t dt   4Integrating Equations = t X SinxX  Interpreting Accuracy Accuracy of IntegrationSpecifying Accuracy 6Integrating Equations 8        8 8Integrating Equations Operations with Complex Numbers Form  2Operations with Complex Numbers Complex StackComplex Operations Functions for One Complex Number, z To Calculate Press Display Description 8  68  6 6 6 4Operations with Complex Numbers Using Complex Numbers in Polar Notation ?  ?  ?  6Operations with Complex Numbers Complex Numbers in Equations 6 ? ?    Program lines ALG modeComplex Number in Program        Vector Arithmetic Vector ArithmeticVector operations  Õ 3    Absolute value of the vector  3  3 3 Dot product   10-4Vector Arithmetic   Angle between vectors Õ 3   10-6Vector Arithmetic Vectors in Equations3   Vectors in Programs Program lines Description 10-8Vector Arithmetic Creating Vectors from Variables or RegistersThen hC Õ hA Menu label Description Base Conversions and Arithmetic and LogicBase Menu Base Conversions and Arithmetic and Logic 11-2Base Conversions and Arithmetic and Logic    Õ  11-4Base Conversions and Arithmetic and Logic Arithmetic in Bases 2, 8,Logic Menu            Representation of NumbersNegative Numbers  Range of Numbers  Using base in program and equationsWindows for Long Binary Numbers    Statistical Operations Statistical OperationsEntering Statistical Data Entering Two-Variable Data Correcting Errors in Data EntryEntering One-Variable Data 12-2Statistical Operations   Initial x, y Corrected x, y Statistics Menus Statistical CalculationsMean Menu Key Description      Sample Standard Deviation     Population Standard Deviation Linear Regression 12-8Statistical Operations  ˆ Õ ˆLinear Regression Menu        12-10Statistical Operations Limitations on Precision of Data Summation Values and the Statistics Registers Summation Statistics Access to the Statistics Registers 12-12Statistical Operations Statistical Operations 12-14Statistical Operations Programming Page Simple Programming Simple Programming Area = πx2 13-2Simple Programming Designing a Program Selecting a ModeKeysDisplay In ALG mode  X  13-4Simple Programming Using RPN, ALG and Equations in ProgramsProgram Boundaries LBL and RTN  letter-key Data Input and Output Strengths of RPN Operations Entering a Program 13-6Simple Programming Clear functions and backspace key 13-8Simple Programming Function Names in ProgramsA R RPN modeE  R   Running a ProgramExecuting a Program XEQ 13-10Simple Programming  Testing a ProgramKeys Display Description RPN mode Entering and Displaying Data 13-12Simple Programming Using Input for Entering Data RPN mode ALG mode 13-14Simple Programming Using View for Displaying Data 13-16Simple Programming Using Equations to Display Messages  ÇR ÇH  V OL  A RE A   Keys RPN mode R H V  R R H   V  S     13-18Simple Programming Displaying Information without Stopping  C  value Programming a Stop or Pause STOP, PSE Error StopsStopping or Interrupting a Program Interrupting a Running Program Editing a Program 13-20Simple Programming Program Memory Viewing Program Memory 13-22Simple Programming Memory UsageCatalog of Programs MEM Clearing One or More Programs Checksum  Nonprogrammable FunctionsProgramming with Base   Numbers Entered in Program Lines Selecting a Base Mode in a ProgramDecimal mode set Ax4 + Bx3 + Cx2 + Dx + E Polynomial Expressions and Horners Method13-26Simple Programming   A X     A  13-28Simple Programming Calling Subroutines XEQ, RTN Programming TechniquesRoutines in Programs Programming Techniques Nested Subroutines 14-2Programming Techniques A2 + b2 + c2 + d2 A2 + B2 Branching GTO14-4Programming Techniques Using GTO from the Keyboard Programmed GTO Instruction Conditional Instructions 14-6Programming Techniques Tests of Comparison x?y, x?0 Test Menus Program Lines Description RPN mode 14-8Programming Techniques Flags Meanings of Flags 14-10Programming Techniques Flag Fraction-Control FlagsClear Programming Techniques Flags Menu 14-12Programming Techniques … takes the natural log of the X-input S  value   value  14-14Programming Techniques Number 14-16Programming Techniques LoopsF      Conditional Loops GTO Loops with Counters DSE, ISG 14-18Programming Techniques Programming Techniques 14-20Programming Techniques Indirectly Addressing Variables and LabelsVariables I and J Indirect Address, I and J If I/J contains Then I/J will address 14-22Programming Techniques Unnamed indirect variables Program Control with I/JEquations with I/J 14-24Programming Techniques Solving and Integrating Programs Solving and Integrating ProgramsSolving a Program 15-2Solving and Integrating Programs V= N x R x T G Keys Display Description ALG modeProgram Lines Description ALG mode P  value   value H       LP   label  variable Using Solve in a Program15-6Solving and Integrating Programs Program Lines In RPN mode Integrating a Program 15-8Solving and Integrating Programs  S   X Sin  label   variable Using Integration in a Program15-10Solving and Integrating Programs Restrictions on Solving and Integrating 15-12Solving and Integrating Programs Statistics Programs Statistics ProgramsCurve Fitting = B + MIn 16-2Statistics Programs Program Listing 16-4Statistics Programs    16-6Statistics Programs Determines if D001 or B001 should be run 16-8Statistics Programs S             Logarithmic Exponential PowerNormal and Inverse-Normal Distributions  Qx = 0.5 − σ 12π xx e−x −x ⎟σ 2 ⎟2dx 16-12Statistics Programs This routine initializes the normal distribution program Program Lines 16-14Statistics Programs Program Lines To the inverse S 16-16Statistics Programs Program D  ∑ x f Grouped Standard Deviation16-18Statistics Programs   16-20Statistics Programs Register Summation Σ f Summation Σ x i f Index variable used to indirectly address the correctStatistics register    U     16-24Statistics Programs Miscellaneous Programs and Equations Miscellaneous Programs and EquationsTime Value of Money TVM equation is I P4 NÕ I 17-4Miscellaneous Programs and Equations KeysDisplay In RPN mode    P  value     I 17-6Miscellaneous Programs and Equations Prime Number Generator   17-8Miscellaneous Programs and Equations Tests to see whether all possible factors have been tried   17-10Miscellaneous Programs and Equations Cross Product in Vectors 17-12Miscellaneous Programs and Equations z 17-14Miscellaneous Programs and Equations Appendixes and Reference Page Calculator Support Support, Batteries, and ServiceSupport, Batteries, and Service A-1 Answers to Common Questions 2Support, Batteries, and Service Environmental Limits Support, Batteries, and Service A-3 Changing the Batteries Testing Calculator Operation 4Support, Batteries, and Service Support, Batteries, and Service A-5 Self-Test 6Support, Batteries, and Service Warranty Support, Batteries, and Service A-7 8Support, Batteries, and Service Customer Support Support, Batteries, and Service A-9 Emea 10Support, Batteries, and Service Support, Batteries, and Service A-11 Invent 12Support, Batteries, and Service Support, Batteries, and Service A-13 Yyyy+ 14Support, Batteries, and Service User Memory and the Stack B-1 User Memory and the StackManaging Calculator Memory Resetting the Calculator 2User Memory and the Stack Clearing Memory User Memory and the Stack B-3 Category DefaultStatus of Stack Lift 4User Memory and the Stack User Memory and the Stack B-5 Disabling OperationsNeutral Operations 6User Memory and the Stack Status of the Last X Registerˆ ˆ Accessing Stack Register Contents 8User Memory and the Stack , ALG SummaryAbout ALG ALG Summary C-1 Doing Two argument Arithmetic in ALG Simple Arithmetic Power Functions Percentage Calculations Quotient and Remainder Of Division Parentheses CalculationsPermutations and Combinations xÕ  4 Õ  Trigonometric Functions Hyperbolic functions Reviewing the Stack ALG Summary C-7 8ALG Summary Integrating an EquationOperations with Complex Numbers 6 ALG Summary C-9  8Ë4 66 6Õ4 6 Entering Statistical Two-Variable Data 12ALG Summary z ΣZ6   ˆ Õ ˆ ALG Summary C-13 14ALG Summary More about Solving D-1 More about SolvingHow Solve Finds a Root 2More about Solving Function Whose Roots Can Be Found Interpreting Results More about Solving D-3 X X  X X  4More about Solving X  XX  6More about Solving XÕ  X Õ  X  X4 More about Solving D-7 8More about Solving When Solve Cannot Find a Root X   More about Solving D-9  X   X  X   10More about Solving X4 X ÕÕ More about Solving D-11 X   12More about Solving More about Solving D-13 Round-Off Error X   14More about Solving More about Integration More about IntegrationHow the Integral Is Evaluated Conditions That Could Cause Incorrect Results 2More about Integration ∞ xe−xdx   4More about Integration More about Integration 6More about Integration Conditions That Prolong Calculation Time   8More about Integration More about Integration 10More about Integration Messages Messages F-1 2Messages Or program. This might take a while Messages F-3 4Messages    Solve include EQN and PGM modecannot find FN each uses a level, they can also generate this error Messages F-5 6Messages Operation Index G-1 Operation IndexName Keys and Description 2Operation Index ×Ø Operation Index G-3 = 4Operation Index Operation Index G-5  Denominator 6Operation Index label Operation Index G-7Natural exponential  Fractional part 8Operation Index  Input variable variable Operation Index G-9  Integer part ISG variable variable LBL label label 10Operation Index Natural logarithm  Pause Operation Index G-11RCL variable Degrees to radians. Returns 2π/360 12Operation Index Operation Index G-13 View variable variable 14Operation IndexHyperbolic Tangent XEQ label label Õ≤ ÕÕ≠ Operation Index G-15 14-7 Menu ≠0? 16Operation Index=y? 11-4 Power Operation Index G-17 18Operation Index Index Index-1 Index-2 Index-3 EQN List TOP 6-7, F-2 Index-4 Index-5 Index-6 Index-7 Index-8 Index-9 Index-10 Index-11 Angle between two vectors Index-12