Solve for z
z=1+3i
z=0
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z=z\left(z-3i\right)
Variable z cannot be equal to 3i since division by zero is not defined. Multiply both sides of the equation by z-3i.
z=z^{2}-3iz
Use the distributive property to multiply z by z-3i.
z-z^{2}=-3iz
Subtract z^{2} from both sides.
z-z^{2}-\left(-3iz\right)=0
Subtract -3iz from both sides.
\left(1+3i\right)z-z^{2}=0
Combine z and 3iz to get \left(1+3i\right)z.
z\left(1+3i-z\right)=0
Factor out z.
z=0 z=1+3i
To find equation solutions, solve z=0 and 1+3i-z=0.
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