- #1
Jessehk
- 21
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I hope this is in the right place.
I'm in grade 12, and I've been given an assignment involving complex numbers.
The question reads:
Use De Moivre's Theorum to verify the identities:
cos(2\theta) = cos^2\theta - sin^2\theta
sin(2\theta) = 2sin\theta cos\theta
I've tried something like this:
<br /> cos(2\theta) + i \cdot sin(2\theta) = (cos\theta + i \cdot sin\theta)^2<br />
<br /> cos(2\theta) + i \cdot sin(2\theta) = cos^2\theta + i \cdot 2cos\theta sin\theta - sin^2\theta<br />
<br /> cos(2\theta) = cos^2\theta - sin^2\theta + i \cdot 2cos\theta sin\theta - i \cdot sin(2\theta)<br />
But I don't understand where to go from there. Can I somehow "separate" them?
Any help would be appreciated.
I'm in grade 12, and I've been given an assignment involving complex numbers.
The question reads:
Use De Moivre's Theorum to verify the identities:
cos(2\theta) = cos^2\theta - sin^2\theta
sin(2\theta) = 2sin\theta cos\theta
I've tried something like this:
<br /> cos(2\theta) + i \cdot sin(2\theta) = (cos\theta + i \cdot sin\theta)^2<br />
<br /> cos(2\theta) + i \cdot sin(2\theta) = cos^2\theta + i \cdot 2cos\theta sin\theta - sin^2\theta<br />
<br /> cos(2\theta) = cos^2\theta - sin^2\theta + i \cdot 2cos\theta sin\theta - i \cdot sin(2\theta)<br />
But I don't understand where to go from there. Can I somehow "separate" them?
Any help would be appreciated.
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