Setting The Calculator To Complex Mode - HP 50g 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 a number written as z = x + iy, where x and y are real
2
numbers, and i is the imaginary unit defined by i
= -1. The complex number
x+iy has a real part, x = Re(z), and an imaginary part, y = Im(z). We can
think of a complex number as a point P(x,y) in the x-y plane, with the x-axis
referred to as the real axis, and the y-axis referred to as the imaginary axis.
Thus, a complex number represented in the form x+iy is said to be in its
Cartesian representation. An alternative Cartesian representation is the ordered
pair z = (x,y). A complex number can also be represented in polar coordinates
i
= r cos + i r sin , where r = |z|
(polar representation) as z = re
2
2
x
y
=
is the magnitude of the complex number z, and
= Arg(z) =
arctan(y/x) is the argument of the complex number z. The relationship between
the Cartesian and polar representation of complex numbers is given by the
i
Euler formula: e
= cos
+ i sin
The complex conjugate of a complex
i
-i
number z = x + iy = re
, is z = x – iy = re
. The complex conjugate of i can
be thought of as the reflection of z about the real (x) axis. Similarly, the
i
negative of z, –z = -x-iy = - re
, can be thought of as the reflection of z about
the origin.

Setting the calculator to COMPLEX mode

When working with complex numbers it is a good idea to set the calculator to
complex mode, using the following keystrokes:
H) @ @CAS@ ˜˜™@ @CHK@
The COMPLEX mode will be selected if the CAS MODES screen shows the
option _Complex checked, i.e.,
Page 4-1  