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Power of a complex number by mathematical induction

Power of a complex number by mathematical induction

IB Year 6 | Grade 12
  1. Use the method of Mathematical Induction to prove that \((1+i)^{4n}=(-1)^n\,2^{2n}\) where \(n\in\mathbb{Z}^{+}\).
  2. Hence find the value of \((1+i)^{20}\).

Solution:

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Answer:(a) Shown; \((1+i)^{4n}=(-1)^n2^{2n}\) (b) \(-1024\)

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