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Page 4-1
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 form) where x and y
are real numbers, and i is the imaginary unit defined by i
2
= -1. The number
has a real part, x = Re(z), and an imaginary part, y = Im(z). The polar form
of a complex number is z = re
i
θ
= r⋅cosθ + i r⋅sinθ, where r = |z|
=
22
yx + is the modulus of the complex number z, and θ = Arg(z) =
arctan(y/x) is the argument of the complex number z. The complex conjugate
of a complex number z = x + iy = re
i
θ
, isz = x – iy = re
-i
θ
. The negative of
z, –z = -x-iy = - re
i
θ
, can be thought of as the reflection of z about the origin.
Setting the calculator to COMPLEX mode
To work with complex numbers select the CAS complex mode:
H)@@CAS@ ˜˜™@@CHK
The COMPLEX mode will be selected if the CAS MODES screen shows the
option _Complex checked off, i.e.,
Press @@OK@@ , twice, to return to the stack.