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  4. If z1=2+3i and z2=1+2i. Then (z1/z2) is equal to

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Q. If $z_{1}=2+3i$ and $z_{2}=1+2i$. Then $\frac{z_{1}}{z_{2}}$ is equal to

Complex Numbers and Quadratic Equations

Solution:

$\frac{z_{1}}{z_{2}}=\left(2+3i\right)\left(\frac{1}{1+2i}\right)$
$=\left(2+3i\right)\left(\frac{1}{5}-\frac{2}{5}i\right)$
$=\left(\frac{2}{5}+\frac{6}{5}\right)+i\left(-\frac{4}{5}+\frac{3}{5}\right)$
$=\frac{8}{5}-\frac{1}{5}i$