z^4+2iz^3+4z^2+2iz+3=0

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Solution for z^4+2iz^3+4z^2+2iz+3=0 equation:


Simplifying
z4 + 2iz3 + 4z2 + 2iz + 3 = 0

Reorder the terms:
3 + 2iz + 2iz3 + 4z2 + z4 = 0

Solving
3 + 2iz + 2iz3 + 4z2 + z4 = 0

Solving for variable 'i'.

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

Add '-3' to each side of the equation.
3 + 2iz + 2iz3 + 4z2 + -3 + z4 = 0 + -3

Reorder the terms:
3 + -3 + 2iz + 2iz3 + 4z2 + z4 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2iz + 2iz3 + 4z2 + z4 = 0 + -3
2iz + 2iz3 + 4z2 + z4 = 0 + -3

Combine like terms: 0 + -3 = -3
2iz + 2iz3 + 4z2 + z4 = -3

Add '-4z2' to each side of the equation.
2iz + 2iz3 + 4z2 + -4z2 + z4 = -3 + -4z2

Combine like terms: 4z2 + -4z2 = 0
2iz + 2iz3 + 0 + z4 = -3 + -4z2
2iz + 2iz3 + z4 = -3 + -4z2

Add '-1z4' to each side of the equation.
2iz + 2iz3 + z4 + -1z4 = -3 + -4z2 + -1z4

Combine like terms: z4 + -1z4 = 0
2iz + 2iz3 + 0 = -3 + -4z2 + -1z4
2iz + 2iz3 = -3 + -4z2 + -1z4

Reorder the terms:
3 + 2iz + 2iz3 + 4z2 + z4 = -3 + -4z2 + -1z4 + 3 + 4z2 + z4

Reorder the terms:
3 + 2iz + 2iz3 + 4z2 + z4 = -3 + 3 + -4z2 + 4z2 + -1z4 + z4

Combine like terms: -3 + 3 = 0
3 + 2iz + 2iz3 + 4z2 + z4 = 0 + -4z2 + 4z2 + -1z4 + z4
3 + 2iz + 2iz3 + 4z2 + z4 = -4z2 + 4z2 + -1z4 + z4

Combine like terms: -4z2 + 4z2 = 0
3 + 2iz + 2iz3 + 4z2 + z4 = 0 + -1z4 + z4
3 + 2iz + 2iz3 + 4z2 + z4 = -1z4 + z4

Combine like terms: -1z4 + z4 = 0
3 + 2iz + 2iz3 + 4z2 + z4 = 0

The solution to this equation could not be determined.

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