HP 15c Manual

 Section 11: Calculating With Complex Numbers 131 
 
One-Number Functions 
The following functions operate on both the real and imaginary parts of the 
number  in  the  X-register,  and  place  the  real  and  imaginary  parts  of  the 
answer back into those registers. 
¤ x N o ∕ @  a : ; 
All trigonometric and hyperbolic functions and their inverses also belong to 
this group.* 
The a function  gives  the  magnitude  of  the  number  in  the  X-registers 
(the  square  root  of  the  sum  of  the...

132 Section 11: Calculating With Complex Numbers 
 
Conditional Tests 
For programming, the four conditional tests below will work in the complex 
sense: ~ and T 0  compare  the complex number  in  the  (real  and 
imaginary)  X-registers  to  0  +  0i,  while T 5  and T 6  compare  the 
complex numbers  in  the  (real  and  imaginary)  X- and  Y-registers.  All  other 
conditional tests besides those listed below ignore the imaginary stack. 
~  T 0 (x ≠ 0)  T 5 (x = y) T 6 (x ≠ y) 
Example:  Complex...

 Section 11: Calculating With Complex Numbers 133 
 
Complex Results from Real Numbers 
In  the  preceding  examples,  the  entry  of  complex  numbers  had  ensured  the 
(automatic)  activation  of  Complex  mode.  There  will  be  times,  however, 
when  you  will  need  Complex  mode  to  perform  certain  operations  on real 
numbers, such as . (Without Complex mode, such as operation would 
result  in  an Error 0 – improper  math  function.)  To  activate  Complex  mode 
at  any  time and  without...

134 Section 11: Calculating With Complex Numbers 
 
 
a + ib = 
r (cos θ + i sin θ) = reiθ (polar) 
rθ (phasor) 
 
; and : can be used to interconvert the rectangular and polar forms of 
a complex number. They operate in Complex mode as follows: 
´ 
; 
converts  the  polar  (or  phasor)  form  of  a  complex  number  to  its 
rectangular  form  by  replacing  the  magnitude r in  the  real  X-
register  with a, and  replacing  the  angle θ in  the  imaginary  X-
register with b. 
| 
: 
converts  the...

 Section 11: Calculating With Complex Numbers 135 
 
Example: Find the  sum 2(cos 65° + i sin 65°)  +  3(cos 40°  + i sin 40°)  and 
express  the  result  in  polar  form,  (In  phasor  form,  evaluate  265° + 
340°.) 
Keystrokes Display  
| D  Sets Degrees mode for any polar-
rectangular conversions. 
2 v 2.0000  
65 ´ V 2.0000 C annunciator displayed; 
Complex mode activated.   
´ ; 0.8452 Converts polar to rectangular 
form; real part (a) displayed. 
3 v 3.0000  
40 ´ V 3.0000  
´ ; 2.2981 Converts...

136 Section 11: Calculating With Complex Numbers 
 
 
Keystrokes Display  
2 ´ }  0.0000 2i. Display shows real part. 
8 “ v -8.0000  
6 ´ V -8.0000 -8 + 6i. 
3 Y  352.0000 (-8 + 6i)3. 
* -1.872.0000 2 i (-8 + 6i)3. 
4 v  4.0000  
5 ¤  2.2361  
2 “ * -4.4721 . 
´ V  4.0000 . 
÷ -295.4551 . 
2 v 5 ¤  2.2361  
4 “ * -8.9443  
´ V  2.0000 . 
÷  9.3982 Real part of result. 
´ % -35.1344 Answer: 9.3982 -35.1344i.   9.3982  
2. Write  a  program  to  evaluate  the  function  for  different 
values of z....

 Section 11: Calculating With Complex Numbers 137 
 
For Further Information 
The HP-15C  Advanced  Functions  Handbook presents  more  detailed  and 
technical  aspects  of  using  complex  numbers  in  various  functions  with  the 
HP-15C. Applications are included. The topics include: 
 Accuracy considerations. 
 Principal branches of multi-valued functions. 
 Complex contour integrals. 
 Complex potentials. 
 Storing and recalling complex numbers using a matrix. 
 Calculating the nth roots of...

 
138 
Section 12 
Calculating With Matrices 
The  HP-15C  enables  you  to  perform  matrix  calculations,  giving  you  the 
capability to  handle  advanced problems  with ease. The  calculator can  work 
with  up  to  five  matrices,  which  are  named A through E since  they  are 
accessed  using the  corresponding A through E keys. The  HP-15C lets 
you  specify  the  size  of  each  matrix,  store  and  recall  the  values  of  matrix 
elements,  and  perform  matrix  operations – for  matrices...

 Section 12: Calculating with Matrices 139 
 
 
Keystrokes Display  
|  8  Deactivates Complex 
mode. 
2 v ´ m A  2.0000 Dimensions matrix A 
to be 2×2. 
´ > 1  2.0000 Prepares for automatic 
entry of matrix 
elements in User mode. 
´ U  2.0000 (Turns on the USER 
annunciator.) 
3.8 O A  A     1,1 Denotes matrix A, row 
1, column 1. (A display 
like this appears 
momentarily as you 
enter each element and 
remains as long as you 
hold the letter key.) 
  3.8000 Stores a11. 
7.2 O A  7.2000 Stores a12....

140 Section 12: Calculating with Matrices 
 
Keystrokes Display  
l > B b 2 1 Enters descriptor for B, the 2×1 
constant matrix. 
l > A A 2 2 Enters descriptor for A, the 2×2 
coefficient matrix, into the X-
register, moving the descriptor 
for B into the Y-register. 
÷ running Temporary display while A-1B is 
being calculated and stored in 
matrix C. 
 C 2 1 Descriptor for the result matrix, 
C, a 2×1 matrix. 
Now  recall  the  elements  of  matrix C – the  solution  to  the  matrix  equation. 
(Also...