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z-2-cos-isin-z-




Question Number 581 by 123456 last updated on 31/Jan/15
z^2 =cos θ+isin θ  z=?
$${z}^{\mathrm{2}} =\mathrm{cos}\:\theta+{i}\mathrm{sin}\:\theta \\ $$$${z}=? \\ $$
Answered by ssahoo last updated on 31/Jan/15
e^(iθ) =cos θ +isin θ=z^2   z=e^((iθ)/2) =cos (θ/2)+isin (θ/2)
$${e}^{{i}\theta} =\mathrm{cos}\:\theta\:+{i}\mathrm{sin}\:\theta={z}^{\mathrm{2}} \\ $$$${z}={e}^{\frac{{i}\theta}{\mathrm{2}}} =\mathrm{cos}\:\frac{\theta}{\mathrm{2}}+{i}\mathrm{sin}\:\frac{\theta}{\mathrm{2}} \\ $$

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