$$(-1+i)(a+bi)=1-3i$$
$a=-2+i-ib$
$$a+bi=\frac{1-3i}{-1+i}$$
$$a+bi=\frac{\left(1-3i\right)\left(-1-i\right)}{\left(-1+i\right)\left(-1-i\right)}$$
$$a+bi=\frac{-4+2i}{2}$$
$$a+bi=-2+i$$
$$a=-2+i-bi$$
$$a=-2+i-ib$$
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$b=ia+\left(1+2i\right)$
$$bi=-2+i-a$$
$$ib=-2+i-a$$
$$\frac{ib}{i}=\frac{-2+i-a}{i}$$
$$b=\frac{-2+i-a}{i}$$
$$b=ia+\left(1+2i\right)$$
