Solve for b
b=ia+\left(3-13i\right)
Solve for a
a=13+3i-ib
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a-4+ib+2i=9+5i
Use the distributive property to multiply b+2 by i.
-4+ib+2i=9+5i-a
Subtract a from both sides.
ib+2i=9+5i-a+4
Add 4 to both sides.
ib+2i=-a+13+5i
Do the additions in 9+5i+4.
ib=-a+13+5i-2i
Subtract 2i from both sides.
ib=-a+13+3i
Do the additions in 13+5i-2i.
ib=13+3i-a
The equation is in standard form.
\frac{ib}{i}=\frac{13+3i-a}{i}
Divide both sides by i.
b=\frac{13+3i-a}{i}
Dividing by i undoes the multiplication by i.
b=ia+\left(3-13i\right)
Divide -a+\left(13+3i\right) by i.
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