If z_1=(4,5) and z_2=(-3,2), then z_1 z_2 equals - Vidyadip

MCQ

If $z_1=(4,5)$ and $z_2=(-3,2)$, then $\frac{z_1}{z_2}$ equals

A
$\left(\frac{-23}{12}, \frac{-2}{13}\right)$
B
$\left(\frac{2}{13}, \frac{-23}{13}\right)$
✓
$\left(\frac{-2}{13}, \frac{-23}{13}\right)$
D
$\left(\frac{-2}{13}, \frac{23}{13}\right)$

✓

Answer

Correct option: C.

$\left(\frac{-2}{13}, \frac{-23}{13}\right)$

(C)
$\frac{z_1}{z_2}=\frac{4+5 i}{-3+2 i} \times \frac{-3-2 i}{-3-2 i}$
$=\frac{-12-8 i -15 i +10}{9-(2 i )^2}$
$=\frac{-2}{13}- i \left(\frac{23}{13}\right)$
$=\left(\frac{-2}{13}, \frac{-23}{13}\right)$

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