HP 15c Manual

 Section 11: Calculating With Complex Numbers 121 
 
Complex mode is activated 
1) automatically, when executing ´ V or ´ }; or 
2) by setting flag 8, the Complex mode flag (|F 8). 
When  the  calculator  is  in  Complex  mode,  the C annunciator  in  the  display 
is lit. This tells you that  flag 8 is set and the complex stack exists. In or out 
of Complex mode, the number appearing in the display is the number in the 
real X-register. 
Note: In Complex mode (signified by the C annunciator), the HP-...

122 Section 11: Calculating With Complex Numbers 
 
Example: Add 2 + 3i and 4 + 5i. (The operations are illustrated in the stack 
diagrams following the keystroke listing.) 
Keystrokes Display  
´ • 4   
2 v 2.0000 Keys real part of first number 
into (real) Y-register. 
3 3 Keys imaginary part of first 
number into (real)  
X-register. 
´ V 2.0000 Creates imaginary stack; moves 
the 3 into the imaginary X-
register, and drops the 2 into the 
real X-register. 
4 v 4.0000 Keys real part of second number...

 Section 11: Calculating With Complex Numbers 123 
 
 
 Re Im  Re Im  Re Im  Re Im  Re Im 
T 9   8   7   7   7 0 
Z 8   7   6   6   7 0 
Y 7   6   2   2   6 0 
X 6   2   2   3   2 3 
Keys: 2 v 3 ´ V 
The execution of ´ V causes the entire stack to drop, the T contents to 
duplicate, and the real X contents to move to the imaginary X-register. 
When  the  second  complex  number  is  entered,  the  stacks  operate  as  shown 
below. Note that v lifts both stacks. 
 
 Re Im  Re Im  Re Im  Re Im 
T 7 0  7 0...

124 Section 11: Calculating With Complex Numbers 
 
Stack Lift in Complex Mode 
Stack  lift  operates  on  the  imaginary  stack  as  it  does  on  the  real  stack  (the 
real  stack  behaves  identically  in  and  out  of  Complex  mode). The  same 
functions that enable, disable, or are  neutral to lifting of the  real stack will 
enable,  disable,  or  be  neutral  to  lifting  of  the  imaginary  stack. (These 
processes are explained in detail in section 3 and appendix B.) 
In  addition, every...

 Section 11: Calculating With Complex Numbers 125 
 
of Complex mode. Instead, you can do either of the following: 
 Multiply by -1. 
 If  you  dont  want  to  disturb  the  rest  of  the  stack,  press “ ´ 
} “ ´ }. 
To find the negative of only one part of a complex number in the X-register: 
 Press “ to negate the real part only. 
 Press ´ } “ ´ } to  negate  the imaginary 
part only, forming the complex conjugate. 
Clearing a Complex Number 
Inevitably you will need to clear a complex number. You...

126 Section 11: Calculating With Complex Numbers 
 
Clearing the Imaginary X-Register. To clear the number in the imaginary 
X-register, press ´ }, then press −. Press ´ } again to 
return the zero, or any new number keyed in, to the imaginary X-register. 
Example: Replace -1 -8i by -1 + 5i. 
 Re Im  Re Im  Re Im  Re Im  Re Im 
T a b  a b  a b  a b  a b 
Z c d  c d  c d  c d  c d 
Y e f  e f  e f  e f  e f 
X -1 -8  -8 -1  0 -1  5 -1  -1 5 
Keys: } − 5 } 
(continue with 
any operation) 
Clearing  the...

 Section 11: Calculating With Complex Numbers 127 
 
Entering  Complex  Numbers  with −.  The  clearing  functions − and 
` can  also  be  used  with } as  an  alternative  method  of  entering 
(and  clearing)  complex  numbers.  Using  this  method,  you  can  enter  a 
complex  number using only  the  X-register, without affecting the  rest of the 
stack.  (This  is  possible  because − and ` disable  stack  lift.) 
Executing } will also create  an imaginary stack if one  is not already 
present....

128 Section 11: Calculating With Complex Numbers 
 
 
 Re Im  Re Im  Re Im  Re Im 
T a b  a b  a b  a b 
Z c d  c d  c d  c d 
Y e f  e f  e f  e f 
X 7 8  0 8  9 8  17 144 
Keys: − 9 | x 
Entering a Real Number 
You have already  seen two  ways of entering a  complex  number. There  is a 
shorter  way  to  enter  a  real  number:  simply  key  it  (or  recall  it)  into  the 
display  just  as  you  would  if  the  calculator  were  not  in  Complex  mode.  As 
you do  so, a  zero  will be  placed in...

 Section 11: Calculating With Complex Numbers 129 
 
Entering a Pure Imaginary Number 
There is a shortcut for entering a pure imaginary number into the X-register 
when you are already in Complex mode: key in the (imaginary) number and 
press ´ } 
Example: Enter  0  +  10i (assuming  the  last  function  executed  was  not − 
or `. 
Keystrokes Display  
10 10 Keys 10 into the displayed 
real X-register and zero into 
the imaginary X-register. 
´ } 0.0000 Exchanges numbers in real 
and imaginary...

130 Section 11: Calculating With Complex Numbers 
 
Storing and Recalling Complex Numbers 
The O and l functions  act  on  the real  X-register  only; therefore, 
the  imaginary  part  of  a  complex  number  must  be  stored  or  recalled 
separately.  The  keystrokes  to  do  this  can  be  entered  as  part  of  a  program 
and executed automatically.* 
To  store a  +  ib from  the  complex  X-register  to  R1 and  R2,  you  can  use  the 
sequence 
O 1  ´}  O 2 
You  can  follow  this  by ´ } to...