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NDA 2023 Maths · Mathematics · Complex Numbers and Quadratic Equations · medium

The imaginary part of the complex number (2+i)/(1-3i) is

Single correct option

The imaginary part of the complex number 2+i1−3i\dfrac{2+i}{1-3i} is
  1. A. 110\dfrac1{10}
  2. B. −710-\dfrac{7}{10}
  3. C. 12\dfrac{1}{2}
  4. D. 710\dfrac{7}{10}
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Answer: (D) 710\dfrac{7}{10}

Multiply by the conjugate: (2+i)(1+3i)(1−3i)(1+3i)=2+6i+i+3i210=−1+7i10\dfrac{(2+i)(1+3i)}{(1-3i)(1+3i)}=\dfrac{2+6i+i+3i^2}{10}=\dfrac{-1+7i}{10}. The imaginary part is 710\frac7{10} (not 7i10\frac{7i}{10}). The negative sign appears only if the conjugate is applied to the wrong factor.
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Original question written in the NDA 2023 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