Page 469 - Schaum's Outline of Theory and Problems of Signals and Systems

456 REVIEW OF COMPLEX NUMBERS

C.2 ADDITION, MULTIPLICATION, AND DMSION
If z, =a, +jb, and z, =a, + jb,, then

z, + z2 = (a, +a,) + j(b, + b,)

zlz2 = (ala2 - b,b2) +j(a,b, + bp,)

(C. 10)

(C. I I)

C.3 THE COMPLEX CONJUGATE

The complex conjugate of z is denoted by z* and is given by

Useful relationships:

1. zz* =r2

4. z-z* =j2Im(z}

C.4 POWERS AND ROOTS OF COMPLEX NUMBERS
The nth power of the complex number z = reie is

n = neine = r "(cos n8 + j sin n8) (C. 13)

from which we have DeMoivre's relation

(C.14)