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The real part of (1)/(2-3i) is Single correct option
The real part of
1 2 − 3 i \dfrac{1}{2-3i} 2 − 3 i 1 is
A. 2 13 \dfrac{2}{13} 13 2 B. 2 5 \dfrac{2}{5} 5 2 C. 3 13 \dfrac{3}{13} 13 3 D. 1 2 \dfrac{1}{2} 2 1 Show answer and solution Answer: (A) 2 13 \dfrac{2}{13} 13 2
Multiply by the conjugate:
1 2 − 3 i = 2 + 3 i 4 + 9 = 2 13 + 3 13 i \frac{1}{2-3i}=\frac{2+3i}{4+9}=\frac{2}{13}+\frac{3}{13}i 2 − 3 i 1 = 4 + 9 2 + 3 i = 13 2 + 13 3 i . The real part is
2 13 \frac2{13} 13 2 . Option
1 2 \frac12 2 1 takes the reciprocal of the real part only, and
3 13 \frac3{13} 13 3 is the imaginary part.
Original question written in the NDA 2017 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