AP EAMCET · Maths · Complex Number
If \(z=\frac{\sqrt{3}+i}{2}\), then \(\left(z^{101}+i^{103}\right)^{105}=\)
- A \(z\)
- B \(z^2\)
- C \(z^3\)
- D \(-z\)
Answer & Solution
Correct Answer
(C) \(z^3\)
Step-by-step Solution
Detailed explanation
We have, \(z=\frac{\sqrt{3}+i}{2} \Rightarrow z=\frac{\sqrt{3}}{2}+\frac{1}{2} i\) \(\Rightarrow \quad z=\cos \frac{\pi}{6}+i \sin \frac{\pi}{6} \Rightarrow z=e^{\frac{i \pi}{6}}\) Now,…
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