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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 representation) 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 representation of a complex number is z = re
i
θ
= r
⋅
cos
θ
+ i r
⋅
sin
θ
,
where r = |z| =
22
yx +
is the magnitude 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
, is
z = 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@
2˜˜™
@@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.