The value of ( -1+i 3 1-i )^ 30 is - Vidyadip

MCQ

The value of $\left(\frac{-1+i \sqrt{3}}{1-i}\right)^{30}$ is

A
$2^{15} i$
B
$-2^{15}$
✓
$-2^{15} i$
D
$6^{5}$

✓

Answer

Correct option: C.

$-2^{15} i$

c
$\left(\frac{-1+i \sqrt{3}}{1-i}\right)^{30}=\left(\frac{2 \omega}{1-i}\right)^{30}$

$=\frac{2^{30} \cdot \omega^{30}}{\left((1- i )^{2}\right)^{30}}$

$=\frac{2^{30} \cdot 1}{\left(1+ i ^{2}-2 i \right)^{15}}$

$=\frac{2^{30}}{-2^{15} \cdot i ^{15}}$

$=-2^{15} i$

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