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9-yi=x+3i
Swap sides so that all variable terms are on the left hand side.
9-iy=x+3i
Multiply -1 and i to get -i.
-iy=x+3i-9
Subtract 9 from both sides.
-iy=x+\left(-9+3i\right)
The equation is in standard form.
\frac{-iy}{-i}=\frac{x+\left(-9+3i\right)}{-i}
Divide both sides by -i.
y=\frac{x+\left(-9+3i\right)}{-i}
Dividing by -i undoes the multiplication by -i.
y=ix+\left(-3-9i\right)
Divide x+\left(-9+3i\right) by -i.