z^2-3(1+z)+5i=0

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Solution for z^2-3(1+z)+5i=0 equation:


Simplifying
z2 + -3(1 + z) + 5i = 0
z2 + (1 * -3 + z * -3) + 5i = 0
z2 + (-3 + -3z) + 5i = 0

Reorder the terms:
-3 + 5i + -3z + z2 = 0

Solving
-3 + 5i + -3z + z2 = 0

Solving for variable 'i'.

Move all terms containing i to the left, all other terms to the right.

Add '3' to each side of the equation.
-3 + 5i + -3z + 3 + z2 = 0 + 3

Reorder the terms:
-3 + 3 + 5i + -3z + z2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 5i + -3z + z2 = 0 + 3
5i + -3z + z2 = 0 + 3

Combine like terms: 0 + 3 = 3
5i + -3z + z2 = 3

Add '3z' to each side of the equation.
5i + -3z + 3z + z2 = 3 + 3z

Combine like terms: -3z + 3z = 0
5i + 0 + z2 = 3 + 3z
5i + z2 = 3 + 3z

Add '-1z2' to each side of the equation.
5i + z2 + -1z2 = 3 + 3z + -1z2

Combine like terms: z2 + -1z2 = 0
5i + 0 = 3 + 3z + -1z2
5i = 3 + 3z + -1z2

Divide each side by '5'.
i = 0.6 + 0.6z + -0.2z2

Simplifying
i = 0.6 + 0.6z + -0.2z2

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