AP EAMCET · Maths · Complex Number
\((1+\sqrt{3} i)^6-(\sqrt{3}+i)^6=\)
- A \(0\)
- B \(32\)
- C \(64\)
- D \(128\)
Answer & Solution
Correct Answer
(D) \(128\)
Step-by-step Solution
Detailed explanation
\( |1+\sqrt{3}i| = 2, \arg(1+\sqrt{3}i) = \frac{\pi}{3} \) \( (1+\sqrt{3}i)^6 = (2e^{i\frac{\pi}{3}})^6 = 2^6 e^{i2\pi} = 64(1) = 64 \) \( |\sqrt{3}+i| = 2, \arg(\sqrt{3}+i) = \frac{\pi}{6} \) \( (\sqrt{3}+i)^6 = (2e^{i\frac{\pi}{6}})^6 = 2^6 e^{i\pi} = 64(-1) = -64 \)…
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