TS EAMCET · Maths · Complex Number
One of the values of \((-64 i)^{5 / 6}\) is
- A \(32 i\)
- B \(16 \sqrt{2}(1+i)\)
- C \(32(1+i)\)
- D \(16 \sqrt{2} i\)
Answer & Solution
Correct Answer
(B) \(16 \sqrt{2}(1+i)\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \text { (b) }(-64 i)^{5 / 6}=(64)^{5 / 6} \times(-i)^{5 / 6} \\ & =32 \times\left(e^{\frac{3 \pi}{2}+2 k \pi}\right)^{5 / 6} \\ & =32 \times e^{\left(\frac{3 \pi}{2}+2 k \pi\right) \frac{5}{6}} \quad \text { (Using De Moivre's Theorem) } \end{aligned}\) Since…
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