User talk:Paul Wormer/scratchbook: Difference between revisions

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{{Image|Complex number.png|right|350px| Complex number ''z'' &equiv; ''r'' exp(''i''&theta;) multiplied by ''i'' gives <i>z'</i> <nowiki>=</nowiki> <i>z</i>&times;''i''
<nowiki>=</nowiki> ''z'' exp(''i''&thinsp;&pi;/2) (counter clockwise rotation over 90°). Division of ''z'' by ''i'' gives ''z''". Division by ''i'' is multiplication by &minus;''i'' <nowiki> = </nowiki> exp(&minus;''i''&thinsp; &pi;/2) (clockwise rotation over 90°).}}

Revision as of 04:31, 19 December 2009

PD Image
Complex number zr exp(iθ) multiplied by i gives z' = z×i = z exp(i π/2) (counter clockwise rotation over 90°). Division of z by i gives z". Division by i is multiplication by −i = exp(−i  π/2) (clockwise rotation over 90°).