1 Complex algebra and the complex plane
Proof. jei j= jcos( ) + isin( )j= q cos2( ) + sin2( ) = 1: In words, this says that ei is always on the unit circle { this is useful to remember! Likewise, if z= rei then jzj= r. You can calculate this, but it should be clear from the de nitions: jzjis the distance from zto the origin, which is exactly the same de nition as for r.
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