Simple Operations With Complex Numbers - HP 50g User Manual

Graphing calculator.

On the other hand, if the coordinate system is set to cylindrical coordinates (use
CYLIN), entering a complex number (x,y), where x and y are real numbers, will
produce a polar representation. For example, in cylindrical coordinates, enter
the number (3.,2.). The figure below shows the RPN stack, before and after
entering this number:

Simple operations with complex numbers

Complex numbers can be combined using the four fundamental operations
(+-*/). The results follow the rules of algebra with the caveat that
2
i
= -1. Operations with complex numbers are similar to those with real
numbers. For example, with the calculator in ALG mode and the CAS set to
Complex, we'll attempt the following sum: (3+5i) + (6-3i):
Notice that the real parts (3+6) and imaginary parts (5-3) are combined
together and the result given as an ordered pair with real part 9 and imaginary
part 2.
Try the following operations on your own:
Notes:
The product of two numbers is represented by: (x
+ i (x
y
+ x
y
1
2
2
The division of two complex numbers is accomplished by multiplying both
numerator and denominator by the complex conjugate of the denominator,
i.e.,
(5-2i) - (3+4i) = (2,-6)
(3-i)·(2-4i) = (2,-14)
(5-2i)/(3+4i) = (0.28,-1.04)
1/(3+4i) = (0.12, -0.16)
).
1
+iy
)(x
+iy
) = (x
1
1
2
2
x
- y
y
)
1
2
1
2
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