Question

If $\frac{a+3i}{2+ib}=1-i$, show that $(5a-7b)=0$.

Answer 1

Let,

$\Rightarrow \frac{a+3i}{2+ib}=1-i$

or, $a+3i=2-2i+ib+b$

or, $(a-b-2)+i(5-b)=0$

Comparing the real and imaginary part of both sides we get,

$\Rightarrow a-b-2=0$ and $5-b=0\Rightarrow b=5$.

Now $b=5$ gives $a=7$.

Now

$(5a-7b)=35-35=0$ [ Using values of $a$ and $b$].