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## Homework Statement

*Use de Moivre's Theorem to express cos3θ in powers of cosθ*

## Homework Equations

z^n = [r(cosθ + isinθ)]^n = r^n (cos(nθ) + i sin(nθ))

## The Attempt at a Solution

cos3θ = Re(cos3θ +isin3θ) = Re[(cosθ +isinθ)^3]

I've then expanded the brackets using binomial theorem and got;

(cosθ)^3 + 3[(cosθ)^2][isinθ] + 3(cosθ)[(isinθ)^2] + (isinθ)^3

So (cosθ)^3 is the real part and 3[(cosθ)^2][isinθ] + 3(cosθ)[(isinθ)^2] + (isinθ)^3 the imaginary part.

If anyone has any suggestions...

Thank you

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