z^2+(1+2i)+(1+7i)=0

Solution for z^2+(1+2i)+(1+7i)=0 equation:

Simplifying
z2 + (1 + 2i) + (1 + 7i) = 0

Remove parenthesis around (1 + 2i)
z2 + 1 + 2i + (1 + 7i) = 0

Remove parenthesis around (1 + 7i)
z2 + 1 + 2i + 1 + 7i = 0

Reorder the terms:
1 + 1 + 2i + 7i + z2 = 0

Combine like terms: 1 + 1 = 2
2 + 2i + 7i + z2 = 0

Combine like terms: 2i + 7i = 9i
2 + 9i + z2 = 0

Solving
2 + 9i + z2 = 0

Solving for variable 'i'.

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

Add '-2' to each side of the equation.
2 + 9i + -2 + z2 = 0 + -2

Reorder the terms:
2 + -2 + 9i + z2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 9i + z2 = 0 + -2
9i + z2 = 0 + -2

Combine like terms: 0 + -2 = -2
9i + z2 = -2

Add '-1z2' to each side of the equation.
9i + z2 + -1z2 = -2 + -1z2

Combine like terms: z2 + -1z2 = 0
9i + 0 = -2 + -1z2
9i = -2 + -1z2

Divide each side by '9'.
i = -0.2222222222 + -0.1111111111z2

Simplifying
i = -0.2222222222 + -0.1111111111z2