Section 3: Calculating In Complex Mode; Using Complex Mode - HP -15C Advanced Functions Handbook

Section 3
Calculating in Complex Mode
Physically important problems involving real data are often solved
by performing relatively simple calculations using complex
numbers. This section gives important insights into complex
computation and shows several examples of solving problems
involving complex numbers.
Using Complex Mode
Complex mode in the HP-15C enables you to evaluate complex-
valued expressions simply. Generally, in Complex mode a
mathematical expression is entered in the same manner as in the
normal "real" mode. For example, consider a program that
evaluates the polynomial P(x) — a
n
x
n
+ ... + aix + a
0
for the value x
in the X-register. By activating Complex mode, this same program
can evaluate P(z), where z is complex. Similarly, other expressions,
such as the Gamma function F(x) in the next example, can be
evaluated for complex arguments in Complex mode.
Example: Write a program that evaluates the continued-fraction
approximation
ln(r(x)) = (x - V^ln x - x + a
0
+ a
:
x + a
2
for the first six values of a:
a
0
=
1
/
2
ln(27r)
a!-1/12
a
2
= 1/30
a
3
= 53/210
a
4
= 195/371
a
5
= 1.011523068
a
6
= 1.517473649.
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