Proof of trigonometric multiplication of complex numbers

embassyhill
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This is supposed to be a proof of trigonometric multiplication of complex numbers:
0I9sN.png

What happened at the =...= point? I understand everything up to that.
 
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embassyhill said:
This is supposed to be a proof of trigonometric multiplication of complex numbers:
0I9sN.png

What happened at the =...= point? I understand everything up to that.

Do the multiplication and see what happens. Bottom part is just equal to r.
 
I did manage to get cos(alpha-beta)+isin(alpha-beta) on the upper part but I was too dumb to remember cos^2+sin^2=1 :P. Thanks.
 

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