JEE Mains · Maths · STD 11 - 4.1 complex nubers
The value of \(\left(\frac{-1+i \sqrt{3}}{1-i}\right)^{30}\) is
- A \(2^{15} i\)
- B \(-2^{15}\)
- C \(-2^{15} i\)
- D \(6^{5}\)
Answer & Solution
Correct Answer
(C) \(-2^{15} i\)
Step-by-step Solution
Detailed explanation
\(\left(\frac{-1+i \sqrt{3}}{1-i}\right)^{30}=\left(\frac{2 \omega}{1-i}\right)^{30}\) \(=\frac{2^{30} \cdot \omega^{30}}{\left((1- i )^{2}\right)^{30}}\) \(=\frac{2^{30} \cdot 1}{\left(1+ i ^{2}-2 i \right)^{15}}\) \(=\frac{2^{30}}{-2^{15} \cdot i ^{15}}\) \(=-2^{15} i\)
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