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HP 49g manual Functions applied to complex numbers, Function Droite equation of a straight line

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Functions applied to complex numbers

Many of the keyboard-based functions and MTH menu functions defined in Chapter 3 for real numbers (e.g., SQ, ,LN, ex, etc.), can be applied to complex numbers. The result is another complex number, as illustrated in the following examples.

Note: When using trigonometric functions and their inverses with complex numbers the arguments are no longer angles. Therefore, the angular measure selected for the calculator has no bearing in the calculation of these functions with complex arguments.

Function DROITE: equation of a straight line

Function DROITE takes as argument two complex numbers, say, x1+iy1 and x2+iy2, and returns the equation of the straight line, say, y = a+bx, that contains the points (x1,y1) and (x2,y2). For example, the line between points A(5,-3) and B(6,2) can be found as follows (example in Algebraic mode):

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HP 49g manual Functions applied to complex numbers, Function Droite equation of a straight line

Contents

Hp 49g+ graphing calculator User’s manualPrinting History Preface Table of Contents Calculations with real numbers Calculations with complex numbers Algebraic and arithmetic operationsSolution to equations Operations with listsVectors Matrices and linear algebraGraphics Calculus ApplicationsMulti-variate Calculus Applications Vector Analysis ApplicationsProbability Distributions Differential EquationsStatistical Applications Limited Warranty W-1 Using SD cardsNumbers in Different Bases Basic Operations Chapter Getting startedBatteries Contents of the calculator’s display Menus Tool menuSetting time and date Introducing the calculator’s keyboardPage Selecting calculator modes Operating Mode √ 3.*5.-1/3.*3./23.3+EXP2.5 Lets try now the expression proposed earlier Number Format and decimal dot or comma Page Page Page Angle Measure Coordinate System Selecting CAS settings Explanation of CAS settings Selecting Display modesSelecting the display font Selecting properties of the line editor Selecting properties of the Stack References Selecting properties of the equation writer EQWChapter Introducing the calculator Calculator objectsEditing expressions in the stack Creating arithmetic expressionsPage Page Creating algebraic expressions 2L 1 + + 2 L + yUsing the Equation Writer EQW to create expressions Page + 2 ⋅ 5 +  x + 2µ ⋅ ∆y  + eHome directory Organizing data in the calculatorSubdirectories Variables Typing variable namesCreating variables Page Page Checking variables contents Page Using function Purge in the stack in Algebraic mode Deleting variablesUndo and CMD functions Using function Purge in the stack in RPN modeChoose boxes vs. Soft Menu Show Prog menu list and select Memory Page References Chapter Calculations with real numbers Examples of real number calculationsPage Page Using powers of 10 in entering data Page Real number functions in the MTH menu Hyperbolic functions and their inversesPage Operations with units Units menuPage Available units Attaching units to numbers Operations with units Page Physical constants in the calculator Unit conversionsEngl Defining and using functions ‘LNx+1 + EXPx ‘ Reference Chapter Calculations with complex numbers Setting the calculator to Complex modeDefinitions Entering complex numbers Polar representation of a complex numberSimple operations with complex numbers Cmplx menus Cmplx menu through the MTH menuCmplx menu in keyboard Functions applied to complex numbers Function Droite equation of a straight lineReference Chapter Algebraic and arithmetic operations Entering algebraic objectsSimple operations with algebraic objects `‚¹ Functions in the ALG menu CollectPage Expansion and factoring using trigonometric functions Expansion and factoring using log-exp functionsOperations with transcendental functions Functions in the Arithmetic menu Polynomials Horner functionVariable Pcoef functionProot function Quot and Remainder functionsPeval function FractionsSIMP2 function Partfrac function Propfrac functionFcoef function Froots function Step-by-step operations with polynomials and fractions− 5X 2 + 3X − Reference Symbolic solution of algebraic equations Chapter Solution to equationsFunction Isol Function Solve Page Function Solvevx Function ZerosNumerical solver menu Polynomial Equations @SOLVE@Solve for coefficients ˜@SYMB@ Financial calculations Solving equations with one unknown through NUM.SLVSolution to simultaneous equations with Mslv Page Reference Chapter Operations with lists Creating and storing listsOperations with lists of numbers Changing signAddition, subtraction, multiplication, division Functions applied to lists Lists of algebraic objects Lists of complex numbersMTH/LIST menu ∆LIST SEQ function MAP functionEntering vectors Chapter VectorsTyping vectors in the stack Using the Matrix Writer Mtrw to enter vectors Storing vectors into variables in the stackPage Page Simple operations with vectors Addition, subtractionMultiplication by a scalar, and division by a scalar Absolute value functionMagnitude MTH/VECTOR menuDot product Cross product Chapter Matrices and linear algebra Using the Matrix WriterEntering matrices in the stack Typing in the matrix directly into the stack Operations with matrices Addition and subtractionMultiplication Cij = ∑aik ⋅ bkj , for i = 1,2,K, m j = 1,2,K, n Page Solution of linear systems Characterizing a matrix The matrix Norm menuFunction DET Function Trace=  a Using the numerical solver for linear systems M x2 Solution with the inverse matrix Solution by division of matricesChapter Graphics Graphs options in the calculatorPlotting an expression of the form y = fx = 1 exp− xGenerating a table of values for a function Page Fast 3D plots Left-1 Right1 Near-1 Far Low High Step Indep Depnd Page Reference Chapter Calculus Applications Calc Calculus menuLimits and derivatives Function limFunctions Deriv and Dervx Xdx = F x + C Anti-derivatives and integralsFunctions INT, INTVX, RISCH, Sigma and Sigmavx Infinite series Definite integralsFunctions TAYLR, TAYLR0, and Series Reference Chapter Multi-variate Calculus Applications Partial derivativesMultiple integrals Φ x, ydydxChapter Vector Analysis Applications Del operatorGradient ∇ = i ⋅ ∂ + j ⋅ ∂ + k ⋅ ∂ ∂x ∂y ∂zDivergence CurlChapter Differential Equations Solution to linear and non-linear equationsCALC/DIFF menu Function Ldec Function Desolve Yx = 5 ⋅ exp−x3 / 3 ⋅ expx3 / 3 ⋅ dx + C0Variable Odetype DesolveLaplace Transforms Laplace transform and inverses in the calculatorFourier series = ∑ c nFunction Fourier Fourier series for a quadratic functionPage Reference Chapter Probability Distributions MTH/PROBABILITY.. sub-menu partFactorials, combinations, and permutations − 2... − + 1 = − rRandom numbers Normal distribution MTH/PROB menu partStudent-t distribution Chi-square distribution F distributionEntering data Chapter Statistical ApplicationsCalculating single-variable statistics Page Obtaining frequency distributions Fitting data to a function y = fx 195238095238 + 2.00857242857*X Correlation Covariance Obtaining additional summary statistics Confidence intervals Page Hypothesis testing Page Reference Base menu Chapter Numbers in Different BasesWriting non-decimal numbers HEX DEC OCT BIN Chapter Using SD cardsStoring objects in the SD card Recalling an object from the SD card Purging an object from the SD cardLimited Warranty Service HP Invent Regulatory information USA