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  4. If z1=6+3 i and z 2=2- i, then ( z 1/ z 2) is equal to

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Q. If $z_{1}=6+3 i$ and $z _{2}=2- i$, then $\frac{ z _{1}}{ z _{2}}$ is equal to

Complex Numbers and Quadratic Equations

Solution:

Let $z_{1}=6+3 i$ and $z_{2}=2-i$
Then,$\frac{z_{1}}{z_{2}}=(6+3 i) \frac{1}{2-i}=\frac{(6+3 i)(2+i)}{(2-i)(2+i)}$
$=(6+3 i)\left(\frac{2}{2^{2}+(-1)^{2}}+i \frac{1}{2^{2}+(-1)^{2}}\right)$
$=(6+3 i)\left(\frac{2}{5}+i \frac{1}{5}\right)=(6+3 i) \frac{(2+i)}{5}$
$=\frac{1}{5}[12-3+ i (6+6)]=\frac{1}{5}(9+12 i )$