Question:medium

Number of real values of $(-1-\sqrt{3}i)^{3/4}$ is

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To find the $n$-th roots of a complex number, always use its general polar form $z=r(\cos(\theta+2k\pi)+i\sin(\theta+2k\pi))$ and then apply De Moivre's theorem for fractional exponents. The distinct roots are found by using $k=0, 1, 2, ..., n-1$. A root is real if its imaginary part ($\sin$ term) is zero.
Updated On: Mar 30, 2026
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The Correct Option is C

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