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NDA 2019 Maths · Mathematics · Complex Numbers and Quadratic Equations · medium

The complex conjugate of ((2+i)^2/(1+i) is

Single correct option

The complex conjugate of (2+i)21+i\dfrac{(2+i)^2}{1+i} is
  1. A. 7+i2\dfrac{7+i}{2}
  2. B. 1−7i2\dfrac{1-7i}{2}
  3. C. 7−i2\dfrac{7-i}{2}
  4. D. 3−4i2\dfrac{3-4i}{2}
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Answer: (C) 7−i2\dfrac{7-i}{2}

First (2+i)2=4+4i−1=3+4i(2+i)^2=4+4i-1=3+4i. Then 3+4i1+i=(3+4i)(1−i)2=3−3i+4i+42=7+i2\dfrac{3+4i}{1+i}=\dfrac{(3+4i)(1-i)}{2}=\dfrac{3-3i+4i+4}{2}=\dfrac{7+i}{2}. The conjugate flips the sign of the imaginary part, giving 7−i2\dfrac{7-i}{2}. The option 7+i2\dfrac{7+i}{2} is the number itself, not its conjugate.
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Original question written in the NDA 2019 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake