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Powers of complex numbers

Powers of complex numbers

IB Year 6 | Grade 12
  1. Evaluate \((1+i)^2\).
  2. Prove by mathematical induction on \(n\) that \((1+i)^{4n} = (-4)^n\), where \(n \in \mathbb{Z}^+\).
  3. Hence find \((1+i)^{32}\).

Solution:

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Answer:(i) \(2i\) (ii) \((1+i)^{4n}=(-4)^n\), proved by induction. (iii) \(65536\).

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