HP 15c - Manual (Page 56)

56
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
+ ... + a
1
x + 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

(x) in the next example, can be evaluated for complex arguments in
Complex mode.
Example: Write a program that evaluates the continued-fraction approximation




    
x
a
x
a
x
a
x x
3
2
1
0
a x - ½)ln x ( )) ( ln(
for the first six values of a:
a
0
= ½ ln(2π)
a
1
= 1/12
a
2
= 1/30
a
3
= 53/210
a
4
= 195/371
a
5
= 1.011523068
a
6
= 1.517473649.
Because this approximation is valid for both real arguments and complex arguments with
Re(z) > 0, this program approximates ln(

(z)) in Complex mode (for sufficiently large |z|).
When |z| > 4 (and Re(z) > 0), the approximation has about 9 or 10 accurate digits.
Enter the following program.
Keystrokes Display
|¥
Program mode.
´CLEARM 000-
´bA 001-42,21,11