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  4. If z1=6+3 i and z2=2-i, then (z1/z2) is equal to (1/a)(9+12 i) The value of 'a' is

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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 $\frac{1}{a}(9+12 i)$ The value of $'a'$ is

Complex Numbers and Quadratic Equations

Solution:

$\frac{z_{1}}{z_{2}}=\frac{6+3 i}{2-i}=\frac{6+3 i}{2-i} \times \frac{2+i}{2+i}=\frac{12+6 i+6 i-3}{4-i^{2}}$
$=\frac{9+12 i}{5}=\frac{1}{5}(9+12 i) \equiv \frac{1}{a}(9+12 i )$
Hence, $a = 5$