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NDA 2016 Maths · Mathematics · Complex Numbers and Quadratic Equations · medium

The square roots of the complex number 3+4i are

Single correct option

The square roots of the complex number 3+4i3+4i are
  1. A. ±(2+i)\pm(2+i)
  2. B. ±(2−i)\pm(2-i)
  3. C. ±(1+2i)\pm(1+2i)
  4. D. ±(3+i)\pm(3+i)
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Answer: (A) ±(2+i)\pm(2+i)

Let (x+iy)2=3+4i(x+iy)^2=3+4i. Then x2−y2=3x^2-y^2=3 and 2xy=42xy=4. Also x2+y2=∣3+4i∣=5x^2+y^2=|3+4i|=5, so x2=4x^2=4, y2=1y^2=1 and, since xy>0xy>0, xx and yy have the same sign. The roots are ±(2+i)\pm(2+i). The option ±(2−i)\pm(2-i) has xy<0xy<0 and squares to 3−4i3-4i.
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Original question written in the NDA 2016 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