z^4+4iz^2-1=0

Solution for z^4+4iz^2-1=0 equation:

Simplifying
z4 + 4iz2 + -1 = 0

Reorder the terms:
-1 + 4iz2 + z4 = 0

Solving
-1 + 4iz2 + z4 = 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 + 4iz2 + 1 + z4 = 0 + 1

Reorder the terms:
-1 + 1 + 4iz2 + z4 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 4iz2 + z4 = 0 + 1
4iz2 + z4 = 0 + 1

Combine like terms: 0 + 1 = 1
4iz2 + z4 = 1

Add '-1z4' to each side of the equation.
4iz2 + z4 + -1z4 = 1 + -1z4

Combine like terms: z4 + -1z4 = 0
4iz2 + 0 = 1 + -1z4
4iz2 = 1 + -1z4

Divide each side by '4z2'.
i = 0.25z-2 + -0.25z2

Simplifying
i = 0.25z-2 + -0.25z2