z^8+2iz^4-1=0

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Solution for z^8+2iz^4-1=0 equation:


Simplifying
z8 + 2iz4 + -1 = 0

Reorder the terms:
-1 + 2iz4 + z8 = 0

Solving
-1 + 2iz4 + z8 = 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 + 2iz4 + 1 + z8 = 0 + 1

Reorder the terms:
-1 + 1 + 2iz4 + z8 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 2iz4 + z8 = 0 + 1
2iz4 + z8 = 0 + 1

Combine like terms: 0 + 1 = 1
2iz4 + z8 = 1

Add '-1z8' to each side of the equation.
2iz4 + z8 + -1z8 = 1 + -1z8

Combine like terms: z8 + -1z8 = 0
2iz4 + 0 = 1 + -1z8
2iz4 = 1 + -1z8

Divide each side by '2z4'.
i = 0.5z-4 + -0.5z4

Simplifying
i = 0.5z-4 + -0.5z4

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