z^2i+4iz+i=0

Solution for z^2i+4iz+i=0 equation:

Simplifying
z2i + 4iz + i = 0

Reorder the terms:
i + 4iz + iz2 = 0

Solving
i + 4iz + iz2 = 0

Solving for variable 'i'.

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

Factor out the Greatest Common Factor (GCF), 'i'.
i(1 + 4z + z2) = 0

Subproblem 1
Set the factor 'i' equal to zero and attempt to solve:

Simplifying
i = 0

Solving
i = 0

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

Simplifying
i = 0
Subproblem 2
Set the factor '(1 + 4z + z2)' equal to zero and attempt to solve:

Simplifying
1 + 4z + z2 = 0

Solving
1 + 4z + z2 = 0

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

Add '-1' to each side of the equation.
1 + 4z + -1 + z2 = 0 + -1

Reorder the terms:
1 + -1 + 4z + z2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4z + z2 = 0 + -1
4z + z2 = 0 + -1

Combine like terms: 0 + -1 = -1
4z + z2 = -1

Add '-4z' to each side of the equation.
4z + -4z + z2 = -1 + -4z

Combine like terms: 4z + -4z = 0
0 + z2 = -1 + -4z
z2 = -1 + -4z

Add '-1z2' to each side of the equation.
z2 + -1z2 = -1 + -4z + -1z2

Combine like terms: z2 + -1z2 = 0
0 = -1 + -4z + -1z2

Simplifying
0 = -1 + -4z + -1z2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
i = {0}