1 - 2i 2 + i + 4 - i 3 + 2i = - Vidyadip

MCQ

$\frac{{1 - 2i}}{{2 + i}} + \frac{{4 - i}}{{3 + 2i}} = $

A
$\frac{{24}}{{13}} + \frac{{10}}{{13}}i$
B
$\frac{{24}}{{13}} - \frac{{10}}{{13}}i$
C
$\frac{{10}}{{13}} + \frac{{24}}{{13}}i$
✓
$\frac{{10}}{{13}} - \frac{{24}}{{13}}i$

✓

Answer

Correct option: D.

$\frac{{10}}{{13}} - \frac{{24}}{{13}}i$

d
(d) $\frac{{1 - 2i}}{{2 + i}} + \frac{{4 - i}}{{3 + 2i}} = \frac{{(1 - 2i)(3 + 2i) + (4 - i)(2 + i)}}{{(2 + i)(3 + 2i)}}$
$ = \frac{{50 - 120i}}{{65}} = \frac{{10}}{{13}} - \frac{{24}}{{13}}i$.

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