Simple operations with complex numbers, Simple operations with complex numbers ,4-4 – HP 50g Graphing Calculator User Manual

Page 171

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Page 4-4

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
i

2

= -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:

(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)

Notes:
The product of two numbers is represented by: (x

1

+iy

1

)(x

2

+iy

2

) = (x

1

x

2

- y

1

y

2

)

+ i (x

1

y

2

+ x

2

y

1

).

The division of two complex numbers is accomplished by multiplying both
numerator and denominator by the complex conjugate of the denominator,
i.e.,

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