Q. If $\frac{(1 + i)^{2}}{2 - i} = x + iy$, then $x + y$ is equal to
A) $- \frac{2}{5}$
B) $\frac{6}{5}$
C) $\frac{2}{5}$
D) $- \frac{6}{5}$
Explanation
(c)
Given, $\frac{(1 + i)^{2}}{2 - i} = x + iy$
$\Rightarrow \ \ \ \ \frac{2i}{2 - i} \times \frac{2 + i}{2 + i} = x + iy$
$\Rightarrow \ \ \ \ \frac{4i - 2}{5} = x + iy$
$\Rightarrow \ \ x + iy = - \frac{2}{5} + \frac{4}{5}i$
$\therefore\ \ \ x + y = - \frac{2}{5} + \frac{4}{5} = \frac{2}{5}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.