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

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


Simplifying
z4 + -2iz2 + 1 = 0

Reorder the terms:
1 + -2iz2 + z4 = 0

Solving
1 + -2iz2 + 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 + -2iz2 + -1 + z4 = 0 + -1

Reorder the terms:
1 + -1 + -2iz2 + z4 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2iz2 + z4 = 0 + -1
-2iz2 + z4 = 0 + -1

Combine like terms: 0 + -1 = -1
-2iz2 + z4 = -1

Add '-1z4' to each side of the equation.
-2iz2 + z4 + -1z4 = -1 + -1z4

Combine like terms: z4 + -1z4 = 0
-2iz2 + 0 = -1 + -1z4
-2iz2 = -1 + -1z4

Divide each side by '-2z2'.
i = 0.5z-2 + 0.5z2

Simplifying
i = 0.5z-2 + 0.5z2

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