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Solve for z, j, k
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z^{2}-2iz+3=z\left(z-i\right)
Consider the first equation. Use the distributive property to multiply z+i by z-3i and combine like terms.
z^{2}-2iz+3=z^{2}-iz
Use the distributive property to multiply z by z-i.
z^{2}-2iz+3-z^{2}=-iz
Subtract z^{2} from both sides.
-2iz+3=-iz
Combine z^{2} and -z^{2} to get 0.
-2iz+3-\left(-iz\right)=0
Subtract -iz from both sides.
-iz+3=0
Combine -2iz and iz to get -iz.
-iz=-3
Subtract 3 from both sides. Anything subtracted from zero gives its negation.
z=\frac{-3}{-i}
Divide both sides by -i.
z=\frac{-3i}{1}
Multiply both numerator and denominator of \frac{-3}{-i} by imaginary unit i.
z=-3i
Divide -3i by 1 to get -3i.
j=2i
Consider the second equation. Calculate 1+i to the power of 2 and get 2i.
k=2i
Consider the third equation. Insert the known values of variables into the equation.
z=-3i j=2i k=2i
The system is now solved.