HP HP-15C - Section 7 Program Editing; Moving to a Line in Program Memory

80 Section 3: Calculating in Complex Mode
3. To calculate higher number roots z/,:
• Press | R/S | to calculate each successive higher-number
root. Each root zk is placed in the complex X-registers and
its number k is placed in the Y-register. Between root
calculations, you can perform other calculations without
disturbing this program (if R2, RS, R4, and the Index
register aren't changed).
• Store the number of the root k in the Index register (using
[STO| Q]), then press |R/S| to calculate zk. The complex root
and its number are placed in the X- and Y-registers,
respectively. (By pressing |R/S| again, you can continue
calculating higher-number roots.)
Example: Use the previous program to compute (1)1/10°. Calculate
ZQ, Zi, and 250 for this expression.
Keystrokes
rglfp/Rl
1001 ENTER 11
EDQjjjfhold)
fR/sl
EGHKhold)
fR/Sl
E M (hold)
Display
Run mode.
1 Enters n = 100 and 2 = 1
(purely real).
1.0000 Calculates 20 (real part).
0.0000 Imaginary part of 20.
0.9980 Calculates z1 (real part).
0.0628 Imaginary part of Z]_.
50.0000 Stores root number in
Index register.
-1.0000 Calculates 250 (real part).
0.0000 Imaginary part of 250.
Solving an Equation for Its Complex Roots
A common method for solving the complex equation f(z) — 0
numerically is Newton's iteration. This method starts with an
approximation ZQ to a root and repeatedly calculates
** + !=**-/(**)//*(**)
until zk converges.
The following example shows how | SOLVE | can be used with
Newton's iteration to estimate complex roots. (A different