Question
Square roots of −i , where i = √−1, are
The correct answer is
\(cos\left(-\frac{\pi}{4}\right)+i\:sin\left(-\frac{\pi}{4}\right), cos\left(\frac{3\pi}{4}\right)+i\:sin\left(\frac{3\pi}{4}\right)\)
Write−i=e⁻ⁱᵖⁱᐟ². Its square roots have angles−π/4 and−π/4+π=3π/4 and unit magnitude. Thus cos(−π/4)+i sin(−π/4) and its negative are the roots.
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