NDA 2024 · PYQ · Complex Numbers · easy
What is (1 + i)⁴ + (1 − i)⁴ equal to, where i = √−1?
Answer
The correct answer is D: −8. (1+i)² = 2i, so (1+i)⁴ = (2i)² = −4. Similarly (1−i)² = −2i, so (1−i)⁴ = (−2i)² = −4.
- A.4
- B.0
- C.−4
- D.−8✓ Correct
(1+i)² = 2i, so (1+i)⁴ = (2i)² = −4. Similarly (1−i)² = −2i, so (1−i)⁴ = (−2i)² = −4. Sum = −4 + (−4) = −8.
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