HP 42S manual Complex Numbers, Complex numbers in rectangular coordinates

5 Complex Numbers

5.1 Complex numbers in rectangular coordinates.

Unlike the HP-33S (and its ancestor HP-32SII) complex numbers are straight supported and used in HP-42S.

There is almost nothing special to say. Just enter -1 and press √x, what are you going to have is

x:0.0000 i1.0000 which means i.

(Just to you have an idea to do the same in HP-33S we have to do

0 ENTER 1 +/- ENTER 0 ENTER .5 CMPLX yx and we will have 0 and 1 meaning i)

Despite it is possible we don't need to calculate the square root of -1 every time, to have i.

We can use ▀ COMPLEX function which take line y and line x of the stack and creates a complex number y+ix.

Again unlike HP-33S almost all functions of HP-42S fully support complex numbers.

Example: Show that i2 is -1.

Solution:

0 ENTER 1 ▀ COMPLEX ▀ x2 which gives -1.0000 i0.0000 (means -1).

5.2 Complex numbers in polar coordinates

When representing a point in R2 we can use any kind of coordinate system. The most more used are the rectangular (or Cartesian system) which use the usual coordinates x and y and the polar system which use the coordinates r and θ.

The relationship between them is

x= r cos θ, y= r sin θ and r2=x2 y2 , tan θ=y/x.

When dealing with complex numbers we can think is real axis as being the x and the imaginary axis as being y and then we can use also polar coordinates.

In this case i will be r=1 and θ=π/2 (90°).

To change between rectangular or polar modes use RECT and POLAR in ▀ MODES menu.