The GATE Grind

GATE 2022 CH – Question 11

Engineering Mathematics · Complex Variables: Complex numbers and polar form · 1 mark · Multiple choice

The value of $(1 + i)^{12}$, where $i = \sqrt{-1}$, is

  1. $-64i$
  2. $64i$
  3. 64
  4. −64

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (D) −64

Explanation

$(1 + i)^2 = 2i$, so $(1 + i)^{12} = (2i)^6 = 64 \times i^6 = 64 \times (-1) = -64$.