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NDA 1 2024 Maths, question 15

Topic: Algebra

Q15

What is (1+i)4+(1−i)4(1+i)^{4}+(1-i)^{4} equal to, where i=−1i=\sqrt{-1} ?

  1. (a) 44
  2. (b) 00
  3. (c) −4-4
  4. (d) −8-8Correct answer

Solution.

Answer: (d) −8-8

  1. (1+i)²=2i, so (1+i)⁴=−4.
  2. Similarly (1−i)²=−2i and (1−i)⁴=−4.
  3. Their sum is −8.