Microwave and Wireless Synthesizers: Theory and Design

APPENDIX A

MATHEMATICAL REVIEW

A-1 FUNCTIONS OF A COMPLEX VARIABLE

Definition:

i or j is also used to indicate reactive components in electrical circuits; i is used in nonelectrical work. A complex number such as

or

can be shown in the complex plane as in Figure A-1. This is called the rectangular form. The magnitude M, as well as the direction or angle θ, can be computed from

or

and

Figure A1 Complex plane showing a complex number as the sum of two components.

or

This is called the polar form. The conversion from one form to the other is achieved by

and

This is the same as

as

We can ...