Question

if (a-2bi)+(b-3ai)=5+2i find a and b

Answer 1

Fell free to ask any doubts or any sort of such problems

Answer 2

a+2bi+b-3ai=5+2i
(a+b)+(2bi-3ai)=5+2i
(a+b)+i(2b-3a)=5+2i

Now for this equation to be true, the real part of LHS must be equal to the real part of RHS and the same with the irrational part.
This means
$a + b = 5 \\ 2a + 2b = 10$
and
$2b - 3a = 2$
Subtracting 2nd equation from 1st, we get
$2a + 2b - 2b + 3a = 8 \\ 5a = 8 \\ a = \frac{8}{5} \\ b = \frac{17}{5}$