# Chapter 4 - Calculations With Complex Numbers; Definitions; Setting The Calculator To Complex Mode - HP 48gII User Manual

Graphing calculator.

Chapter 4
Calculations with complex numbers
This chapter shows examples of calculations and application of functions to
complex numbers.

### Definitions

A complex number z is written as z = x + iy, (Cartesian representation) where
x and y are real numbers, and i is the imaginary unit defined by i
number has a real part, x = Re(z), and an imaginary part, y = Im(z). The
polar representation of a complex number is z = re
x +
2
where r = |z| =
= Arg(z) = arctan(y/x) is the argument of the complex number z. The
complex conjugate of a complex number z = x + iy = re
θ
i
. The negative of z, –z = -x-iy = - re

### Setting the calculator to COMPLEX mode

To work with complex numbers select the CAS complex mode:
The COMPLEX mode will be selected if the CAS MODES screen shows the
option _Complex checked off, i.e.,
2
y
is the magnitude of the complex number z, and
θ
i
, can be thought of as the reflection of
H) @ @CAS@ 2˜˜™ @@CHK@
2
= -1. The
θ
θ
θ,
i
= r
cos
+ i r
sin
θ
i
, is
z = x – iy = re
Page 4-1
θ
-  