Electricity and Magnetism · Problem 8.7

MAXWELL'S EQUATIONS AND ELECTROMAGNETIC WAVES — Edward Purcell & David Morin

Physics — E&M · magnitude-and-phase

Problem

Show that

a + bi

can be written as

I_0 e^{i\phi}

, where

I_0 = \sqrt{a^2 + b^2}

and

\phi = \tan^{-1}(b/a)