The value of ( - i)^ 1/3 is - Vidyadip

MCQ

The value of ${( - i)^{1/3}}$ is

A
$\frac{{1 + \sqrt 3 i}}{2}$
B
$\frac{{\sqrt 3 - i}}{2}$
C
$\frac{{ - \sqrt 3 - i}}{2}$
✓
$(b) $ and $ (c)$ both

✓

Answer

Correct option: D.

$(b) $ and $ (c)$ both

d
(d) Since $\frac{{ - \sqrt 3 - i}}{2} = - \left( {\cos \frac{\pi }{6} + i\sin \frac{\pi }{6}} \right)$
==> ${\left( {\frac{{ - \sqrt 3 - i}}{2}} \right)^3} = - {\left( {\cos \frac{\pi }{6} + i\sin \frac{\pi }{6}} \right)^3} = - i$
and $\frac{{\sqrt 3 - i}}{2} = \cos \frac{\pi }{6} - i\sin \frac{\pi }{6}$
and ${\left( {\frac{{\sqrt 3 - i}}{2}} \right)^3} = \cos \frac{\pi }{2} - i\sin \frac{\pi }{2} = - i$.
Hence the result.

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