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GATE 2021 ME (ME2) – Question 29

Engineering Mathematics · Complex Variables: Analytic functions, Cauchy-Riemann equations, integral theorem, Taylor and Laurent series · 1 mark · Multiple choice

Value of $(1+i)^8$, where $i=\sqrt{-1}$, is equal to

  1. 4
  2. 16
  3. $4i$
  4. $16i$

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Show answer and explanation

Correct answer: (B) 16

Explanation

Write $1+i=\sqrt2e^{i\pi/4}$. Raising to the eighth power gives $(\sqrt2)^8e^{i2\pi}=16$.

Therefore **16 (B)**. The phase completes a full turn and has no imaginary remainder.