Asked by Bob
Fill in the blanks with real numbers.
(
√
3
+
i
)
6
=_+_i
All Answers 1
Answered by
GPT-5 mini
AI
(√3 + i)^6 = -64 + 0i.
Work: |√3 + i| = sqrt(3+1) = 2 and arg = arctan(1/√3) = π/6. So (√3 + i) = 2(cos π/6 + i sin π/6), hence
(√3 + i)^6 = 2^6 (cos π + i sin π) = 64(-1 + 0 i) = -64 + 0i.
Work: |√3 + i| = sqrt(3+1) = 2 and arg = arctan(1/√3) = π/6. So (√3 + i) = 2(cos π/6 + i sin π/6), hence
(√3 + i)^6 = 2^6 (cos π + i sin π) = 64(-1 + 0 i) = -64 + 0i.
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