z^2+z+1+i=0

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

Simplifying
z2 + z + 1 + i = 0

Reorder the terms:
1 + i + z + z2 = 0

Solving
1 + i + z + z2 = 0

Solving for variable 'i'.

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

Add '-1' to each side of the equation.
1 + i + z + -1 + z2 = 0 + -1

Reorder the terms:
1 + -1 + i + z + z2 = 0 + -1

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

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

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

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

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

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

Simplifying
i = -1 + -1z + -1z2