Question:
\[
(1 + 2i)^6 \text{ is equal to:}
\]
\[
(1 + 2i)^6 \text{ is equal to:}
\]
Updated On: Mar 30, 2025
- None of these
- \(177 + 44i\)
- \(177 + 44j\)
- \(177 - 44i\)
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The Correct Option is A
Solution and Explanation
Convert to polar form: \[ r = \sqrt{1^2 + 2^2} = \sqrt{5},\quad \theta = \tan^{-1}(2) \] Then, \[ (1 + 2i)^6 = r^6 \cdot \text{cis}(6\theta) = 5^3 \cdot \text{cis}(6 \tan^{-1}(2)) \] Evaluate using calculator or De Moivre’s theorem. Result is neither matching any of the options.
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