$$(6+5i)(a+bi)=38-9i$$
$a=3-4i-ib$
$$a+bi=\frac{38-9i}{6+5i}$$
$$a+bi=\frac{\left(38-9i\right)\left(6-5i\right)}{\left(6+5i\right)\left(6-5i\right)}$$
$$a+bi=\frac{183-244i}{61}$$
$$a+bi=3-4i$$
$$a=3-4i-bi$$
$$a=3-4i-ib$$
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$b=ia+\left(-4-3i\right)$
$$bi=3-4i-a$$
$$ib=3-4i-a$$
$$\frac{ib}{i}=\frac{3-4i-a}{i}$$
$$b=\frac{3-4i-a}{i}$$
$$b=ia+\left(-4-3i\right)$$
