z^4+8(1+i)z^2-4(3-4i)=0

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Solution for z^4+8(1+i)z^2-4(3-4i)=0 equation:


Simplifying
z4 + 8(1 + i) * z2 + -4(3 + -4i) = 0

Reorder the terms for easier multiplication:
z4 + 8z2(1 + i) + -4(3 + -4i) = 0
z4 + (1 * 8z2 + i * 8z2) + -4(3 + -4i) = 0

Reorder the terms:
z4 + (8iz2 + 8z2) + -4(3 + -4i) = 0
z4 + (8iz2 + 8z2) + -4(3 + -4i) = 0
z4 + 8iz2 + 8z2 + (3 * -4 + -4i * -4) = 0
z4 + 8iz2 + 8z2 + (-12 + 16i) = 0

Reorder the terms:
-12 + 16i + 8iz2 + 8z2 + z4 = 0

Solving
-12 + 16i + 8iz2 + 8z2 + z4 = 0

Solving for variable 'i'.

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

Add '12' to each side of the equation.
-12 + 16i + 8iz2 + 8z2 + 12 + z4 = 0 + 12

Reorder the terms:
-12 + 12 + 16i + 8iz2 + 8z2 + z4 = 0 + 12

Combine like terms: -12 + 12 = 0
0 + 16i + 8iz2 + 8z2 + z4 = 0 + 12
16i + 8iz2 + 8z2 + z4 = 0 + 12

Combine like terms: 0 + 12 = 12
16i + 8iz2 + 8z2 + z4 = 12

Add '-8z2' to each side of the equation.
16i + 8iz2 + 8z2 + -8z2 + z4 = 12 + -8z2

Combine like terms: 8z2 + -8z2 = 0
16i + 8iz2 + 0 + z4 = 12 + -8z2
16i + 8iz2 + z4 = 12 + -8z2

Add '-1z4' to each side of the equation.
16i + 8iz2 + z4 + -1z4 = 12 + -8z2 + -1z4

Combine like terms: z4 + -1z4 = 0
16i + 8iz2 + 0 = 12 + -8z2 + -1z4
16i + 8iz2 = 12 + -8z2 + -1z4

Reorder the terms:
-12 + 16i + 8iz2 + 8z2 + z4 = 12 + -8z2 + -1z4 + -12 + 8z2 + z4

Reorder the terms:
-12 + 16i + 8iz2 + 8z2 + z4 = 12 + -12 + -8z2 + 8z2 + -1z4 + z4

Combine like terms: 12 + -12 = 0
-12 + 16i + 8iz2 + 8z2 + z4 = 0 + -8z2 + 8z2 + -1z4 + z4
-12 + 16i + 8iz2 + 8z2 + z4 = -8z2 + 8z2 + -1z4 + z4

Combine like terms: -8z2 + 8z2 = 0
-12 + 16i + 8iz2 + 8z2 + z4 = 0 + -1z4 + z4
-12 + 16i + 8iz2 + 8z2 + z4 = -1z4 + z4

Combine like terms: -1z4 + z4 = 0
-12 + 16i + 8iz2 + 8z2 + z4 = 0

The solution to this equation could not be determined.

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