( 1 1 - 2i + 3 1 + i ) , , ( 3 + 4i 2 - 4i ) = - Vidyadip

MCQ

$\left( {\frac{1}{{1 - 2i}} + \frac{3}{{1 + i}}} \right)\,\,\left( {\frac{{3 + 4i}}{{2 - 4i}}} \right) = $

A
$\frac{1}{2} + \frac{9}{2}i$
B
$\frac{1}{2} - \frac{9}{2}i$
C
$\frac{1}{4} - \frac{9}{4}i$
✓
$\frac{1}{4} + \frac{9}{4}i$

✓

Answer

Correct option: D.

$\frac{1}{4} + \frac{9}{4}i$

d
(d)$\left( {\frac{1}{{1 - 2i}} + \frac{3}{{1 + i}}} \right)\,\,\left( {\frac{{3 + 4i}}{{2 - 4i}}} \right)$
$ = \left[ {\frac{{1 + 2i}}{{{1^2} + {2^2}}} + \frac{{3 - 3i}}{{{1^2} + {1^2}}}} \right]\,\left[ {\frac{{6 - 16 + 12i + 8i}}{{{2^2} + {4^2}}}} \right]$
$ = \left( {\frac{{2 + 4i + 15 - 15i}}{{10}}} \right)\,\,\left( {\frac{{ - 1 + 2i}}{2}} \right)$
$ = \frac{{(17 - 11i)( - 1 + 2i)}}{{20}} = \frac{{5 + 45i}}{{20}} = \frac{1}{4} + \frac{9}{4}i$.

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