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Find the real part of the complex number (i-1)^3 by using De Moivre's formula
My lecture notes is too brief need help !
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Write it in the polar form:
$\displaystyle \displaystyle (i-1)^3 = \bigg[\sqrt{2}\left(\cos\left(\frac{3\pi}{4}\right)+i\si n\left(\frac{3\pi}{4}\right)\right)\bigg]^3$.
De Moivre's theorem tells you that, for any arbitrary $\displaystyle x$ and integer $\displaystyle n$, we have:
$\displaystyle \left(\cos{x}+i\sin{x}\right)^n = \cos\left(nx\right)+i\sin\left(nx\right)$.