z^4+(15+7i)z^2+8=0

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Solution for z^4+(15+7i)z^2+8=0 equation:


Simplifying
z4 + (15 + 7i) * z2 + 8 = 0

Reorder the terms for easier multiplication:
z4 + z2(15 + 7i) + 8 = 0
z4 + (15 * z2 + 7i * z2) + 8 = 0

Reorder the terms:
z4 + (7iz2 + 15z2) + 8 = 0
z4 + (7iz2 + 15z2) + 8 = 0

Reorder the terms:
8 + 7iz2 + 15z2 + z4 = 0

Solving
8 + 7iz2 + 15z2 + z4 = 0

Solving for variable 'i'.

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

Add '-8' to each side of the equation.
8 + 7iz2 + 15z2 + -8 + z4 = 0 + -8

Reorder the terms:
8 + -8 + 7iz2 + 15z2 + z4 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 7iz2 + 15z2 + z4 = 0 + -8
7iz2 + 15z2 + z4 = 0 + -8

Combine like terms: 0 + -8 = -8
7iz2 + 15z2 + z4 = -8

Add '-15z2' to each side of the equation.
7iz2 + 15z2 + -15z2 + z4 = -8 + -15z2

Combine like terms: 15z2 + -15z2 = 0
7iz2 + 0 + z4 = -8 + -15z2
7iz2 + z4 = -8 + -15z2

Add '-1z4' to each side of the equation.
7iz2 + z4 + -1z4 = -8 + -15z2 + -1z4

Combine like terms: z4 + -1z4 = 0
7iz2 + 0 = -8 + -15z2 + -1z4
7iz2 = -8 + -15z2 + -1z4

Divide each side by '7z2'.
i = -1.142857143z-2 + -2.142857143 + -0.1428571429z2

Simplifying
i = -1.142857143z-2 + -2.142857143 + -0.1428571429z2

Reorder the terms:
i = -2.142857143 + -1.142857143z-2 + -0.1428571429z2

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