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TS EAMCET · Maths · Complex Number

\((1-i \sqrt{3})^{2025}=\)

  1. A \(2^{2025}\)
  2. B \(2^{2026}\)
  3. C \(-2^{2025}\)
  4. D \(-2^{2026}\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(-2^{2025}\)

Step-by-step Solution

Detailed explanation

\(1-i\sqrt{3} = 2\left(\cos\left(-\frac{\pi}{3}\right)+i\sin\left(-\frac{\pi}{3}\right)\right)\) \((1-i\sqrt{3})^{2025} = \left[2\left(\cos\left(-\frac{\pi}{3}\right)+i\sin\left(-\frac{\pi}{3}\right)\right)\right]^{2025}\)…