# TITLE:  Complex Trig,Logs,Exponential & Powers
# AUTHOR: Roy F.A. Maclean 
# EMAIL:  rfamgm at gmail
# WEB:    http://www.spiderpixel.co.uk/caspro         
# DATE:   9700version 96/97?, 9850version:26Feb1997, combined:26Feb1998, 22May1999        
# MAKE:   CASIO   
# MODEL:  9700 or later
# SIZE:   226 over two areas
#
# With this program you can find the exponential, log, sin, cos, sinh, cosh
# of a complex number, or raise to a complex power.
# A menu is displayed. Enter 1-7 to make choice.
# If you enter 7 then you will be prompted for the power you wish to raise to.
# Z & N can be real or complex.
# If you want Z^N then Z must be nonzero for this program.
# Zero raised to anything is zero of course.
#
# The formulae that this program uses are:
# let z=x+iy, then e^z = (e^x)(cos y + i*sin y)
# proof: e^z=e^(x+iy)=(e^x)(e^iy)=(e^x)(cos y +i*siny)
#
# ln(z)=ln(abs z)+i*arg(z)
#
# z^n=e^(n*ln(z))
#
# sin(z)=(e^(iz)-e^(-iz))/2i  cos(z)=(e^(iz)+e^(-iz))/2
#
# sinh(z)=(e^z-e^(-z))/2      cosh(z)=(e^z+e^(-z))/2
#
# Imp & Rep are on the complex menu. 
# e^ is the inverse natural log on <shift><ln> button.
#
#   \i is the complex i
#   use reciprocal sign for \^-1
#

@@ Program 1

Lbl 0
Rad
"e ln S C SH CH ^"
"1 2  3 4 5 6 7"?->A
"Z"?->Z
Z:Prog 2:Ans->C   
-Z:Prog 2:Ans->D
\iZ:Prog 2:Ans->E                       
-\iZ:Prog 2:Ans->F
Frac 14A\^-1=0=>ln Abs Z+\i*Arg Z->H   
A=1=>C_
A=2=>H_
A=3=>(E-F)/2\i_                
A=4=>(E+F)/2_
A=5=>(C-D)/2_
A=6=>(C+D)/2_
A<>7=>Goto 0
"N"?->N:NH:Prog 2
Ans_
Goto 0


@@ Program 2

(cos ImP Ans+\i*sin ImP Ans)e^ReP Ans