CALCULUS Understanding Its Concepts and Methods

Argument

A complex number *z* = *x* + *iy* can be thought
of as a point (*x*,*y*)
in the plane.

In polar coordinates, *x* = *r* cos *t* and *x* = *r* sin *t*.

Thus any complex number can be written as
*z* = *x* + *iy = r*
cos *t * + *ir* sin *t* = *r* (cos *t
*+ *i* sin *t)* where

The angle *t
*is called the amplitude
or argument of *z*.

The argument is not unique, but any two
arguments of *z* differ
by an integer multiple of 2*p*.

The argument that lies between between *-p* and *p*
is denoted by arg *z*.

For example,

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Copyright © 2006 Darel Hardy, Fred Richman, Carol Walker, Robert Wisner. All rights reserved. Except upon the express prior permission in writing, from the authors, no part of this work may be reproduced, transcribed, stored electronically, or transmitted in any form by any method.