Proof of trigonometric multiplication of complex numbers

AI Thread Summary
The discussion focuses on the proof of trigonometric multiplication of complex numbers, specifically addressing confusion at a certain point in the proof. Participants encourage performing the multiplication to clarify the process, noting that the denominator simplifies to r. One contributor successfully derives cos(alpha-beta) + i*sin(alpha-beta) but overlooks the identity cos^2 + sin^2 = 1, which is crucial for completing the proof. The conversation highlights the importance of understanding the relationship between trigonometric identities and complex number multiplication. Overall, the discussion emphasizes the need for clarity in mathematical proofs involving 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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