Question

$ (1 + 2i)^6 $ is equal to:

• A. None of these
• B. \(177 + 44i\)
• C. \(177 + 44j\)
• D. \(177 - 44i\)

Answer 1

The Correct Option is A

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.