Z^4+(5-14i)z^2-(24+10i)=0

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Solution for Z^4+(5-14i)z^2-(24+10i)=0 equation: 


Simplifying
Z4 + (5 + -14i) * z2 + -1(24 + 10i) = 0

Reorder the terms for easier multiplication:
Z4 + z2(5 + -14i) + -1(24 + 10i) = 0
Z4 + (5 * z2 + -14i * z2) + -1(24 + 10i) = 0

Reorder the terms:
Z4 + (-14iz2 + 5z2) + -1(24 + 10i) = 0
Z4 + (-14iz2 + 5z2) + -1(24 + 10i) = 0
Z4 + -14iz2 + 5z2 + (24 * -1 + 10i * -1) = 0
Z4 + -14iz2 + 5z2 + (-24 + -10i) = 0

Reorder the terms:
-24 + Z4 + -10i + -14iz2 + 5z2 = 0

Solving
-24 + Z4 + -10i + -14iz2 + 5z2 = 0

Solving for variable 'Z'.

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

Add '24' to each side of the equation.
-24 + Z4 + -10i + -14iz2 + 24 + 5z2 = 0 + 24

Reorder the terms:
-24 + 24 + Z4 + -10i + -14iz2 + 5z2 = 0 + 24

Combine like terms: -24 + 24 = 0
0 + Z4 + -10i + -14iz2 + 5z2 = 0 + 24
Z4 + -10i + -14iz2 + 5z2 = 0 + 24

Combine like terms: 0 + 24 = 24
Z4 + -10i + -14iz2 + 5z2 = 24

Add '10i' to each side of the equation.
Z4 + -10i + -14iz2 + 10i + 5z2 = 24 + 10i

Reorder the terms:
Z4 + -10i + 10i + -14iz2 + 5z2 = 24 + 10i

Combine like terms: -10i + 10i = 0
Z4 + 0 + -14iz2 + 5z2 = 24 + 10i
Z4 + -14iz2 + 5z2 = 24 + 10i

Add '14iz2' to each side of the equation.
Z4 + -14iz2 + 14iz2 + 5z2 = 24 + 10i + 14iz2

Combine like terms: -14iz2 + 14iz2 = 0
Z4 + 0 + 5z2 = 24 + 10i + 14iz2
Z4 + 5z2 = 24 + 10i + 14iz2

Add '-5z2' to each side of the equation.
Z4 + 5z2 + -5z2 = 24 + 10i + 14iz2 + -5z2

Combine like terms: 5z2 + -5z2 = 0
Z4 + 0 = 24 + 10i + 14iz2 + -5z2
Z4 = 24 + 10i + 14iz2 + -5z2

Simplifying
Z4 = 24 + 10i + 14iz2 + -5z2

Reorder the terms:
-24 + Z4 + -10i + -14iz2 + 5z2 = 24 + 10i + 14iz2 + -5z2 + -24 + -10i + -14iz2 + 5z2

Reorder the terms:
-24 + Z4 + -10i + -14iz2 + 5z2 = 24 + -24 + 10i + -10i + 14iz2 + -14iz2 + -5z2 + 5z2

Combine like terms: 24 + -24 = 0
-24 + Z4 + -10i + -14iz2 + 5z2 = 0 + 10i + -10i + 14iz2 + -14iz2 + -5z2 + 5z2
-24 + Z4 + -10i + -14iz2 + 5z2 = 10i + -10i + 14iz2 + -14iz2 + -5z2 + 5z2

Combine like terms: 10i + -10i = 0
-24 + Z4 + -10i + -14iz2 + 5z2 = 0 + 14iz2 + -14iz2 + -5z2 + 5z2
-24 + Z4 + -10i + -14iz2 + 5z2 = 14iz2 + -14iz2 + -5z2 + 5z2

Combine like terms: 14iz2 + -14iz2 = 0
-24 + Z4 + -10i + -14iz2 + 5z2 = 0 + -5z2 + 5z2
-24 + Z4 + -10i + -14iz2 + 5z2 = -5z2 + 5z2

Combine like terms: -5z2 + 5z2 = 0
-24 + Z4 + -10i + -14iz2 + 5z2 = 0

The solution to this equation could not be determined.

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