z^4-(1-i)z^2+12i=0

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Solution for z^4-(1-i)z^2+12i=0 equation:


Simplifying
z4 + -1(1 + -1i) * z2 + 12i = 0

Reorder the terms for easier multiplication:
z4 + -1z2(1 + -1i) + 12i = 0
z4 + (1 * -1z2 + -1i * -1z2) + 12i = 0

Reorder the terms:
z4 + (1iz2 + -1z2) + 12i = 0
z4 + (1iz2 + -1z2) + 12i = 0

Reorder the terms:
12i + 1iz2 + -1z2 + z4 = 0

Solving
12i + 1iz2 + -1z2 + z4 = 0

Solving for variable 'i'.

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

Add 'z2' to each side of the equation.
12i + 1iz2 + -1z2 + z2 + z4 = 0 + z2

Combine like terms: -1z2 + z2 = 0
12i + 1iz2 + 0 + z4 = 0 + z2
12i + 1iz2 + z4 = 0 + z2
Remove the zero:
12i + 1iz2 + z4 = z2

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

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

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

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

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

The solution to this equation could not be determined.

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