Solve for b
b=3i+\frac{8+2i}{z}
z\neq 0
Solve for z
z=\frac{-2+8i}{ib+3}
b\neq 3i
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z\left(ib+3\right)=-2+8i
Variable b cannot be equal to 3i since division by zero is not defined. Multiply both sides of the equation by ib+3.
izb+3z=-2+8i
Use the distributive property to multiply z by ib+3.
izb=-2+8i-3z
Subtract 3z from both sides.
\frac{izb}{iz}=\frac{-2+8i-3z}{iz}
Divide both sides by iz.
b=\frac{-2+8i-3z}{iz}
Dividing by iz undoes the multiplication by iz.
b=3i+\frac{8+2i}{z}
Divide -2+8i-3z by iz.
b=3i+\frac{8+2i}{z}\text{, }b\neq 3i
Variable b cannot be equal to 3i.
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