Question

If $w=3-2i$ and $z=-2+4i$, then $\frac{w}{z}$ can be written as $a+bi$, which is equivalent to

• A. $-\frac{3}{2}-\frac{1}{2}i$
• B. $-\frac{7}{10}-\frac{2}{5}i$
• C. $\frac{13}{20}-\frac{1}{2}i$
• D. $\frac{7}{6}+\frac{2}{3}i$

Answer 1

Answer: (B)

$-\frac{7}{10}-\frac{2}{5}i$

Given, $w=3-2i$ and $z=-2+4i$

$\therefore \frac{w}{z}=\frac{3-2i}{-2+4i}$

Taking conjugate, we get

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

$=$ $\frac{-6-12i+4i+8i^2}{(-2{)}^2-(4i{)}^2}$

$=$ $\frac{-6-8i-8}{4+16}$

$=$ $\frac{-14-8i}{20}$

Taking $2$ as common, we get

$=$ $\frac{-7-4i}{10}$

$\frac{w}{z}=\frac{-7}{10}-\frac{2i}{5}$ is in the form of $a+bi$