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Simplifying Z3 + -1(4i + 4) * z2 + (12i + -2) * z + 8 + -4i = 0 Reorder the terms: Z3 + -1(4 + 4i) * z2 + (12i + -2) * z + 8 + -4i = 0 Reorder the terms for easier multiplication: Z3 + -1z2(4 + 4i) + (12i + -2) * z + 8 + -4i = 0 Z3 + (4 * -1z2 + 4i * -1z2) + (12i + -2) * z + 8 + -4i = 0 Reorder the terms: Z3 + (-4iz2 + -4z2) + (12i + -2) * z + 8 + -4i = 0 Z3 + (-4iz2 + -4z2) + (12i + -2) * z + 8 + -4i = 0 Reorder the terms: Z3 + -4iz2 + -4z2 + (-2 + 12i) * z + 8 + -4i = 0 Reorder the terms for easier multiplication: Z3 + -4iz2 + -4z2 + z(-2 + 12i) + 8 + -4i = 0 Z3 + -4iz2 + -4z2 + (-2 * z + 12i * z) + 8 + -4i = 0 Reorder the terms: Z3 + -4iz2 + -4z2 + (12iz + -2z) + 8 + -4i = 0 Z3 + -4iz2 + -4z2 + (12iz + -2z) + 8 + -4i = 0 Reorder the terms: 8 + Z3 + -4i + 12iz + -4iz2 + -2z + -4z2 = 0 Solving 8 + Z3 + -4i + 12iz + -4iz2 + -2z + -4z2 = 0 Solving for variable 'Z'. Move all terms containing Z to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + Z3 + -4i + 12iz + -4iz2 + -2z + -8 + -4z2 = 0 + -8 Reorder the terms: 8 + -8 + Z3 + -4i + 12iz + -4iz2 + -2z + -4z2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + Z3 + -4i + 12iz + -4iz2 + -2z + -4z2 = 0 + -8 Z3 + -4i + 12iz + -4iz2 + -2z + -4z2 = 0 + -8 Combine like terms: 0 + -8 = -8 Z3 + -4i + 12iz + -4iz2 + -2z + -4z2 = -8 Add '4i' to each side of the equation. Z3 + -4i + 12iz + -4iz2 + -2z + 4i + -4z2 = -8 + 4i Reorder the terms: Z3 + -4i + 4i + 12iz + -4iz2 + -2z + -4z2 = -8 + 4i Combine like terms: -4i + 4i = 0 Z3 + 0 + 12iz + -4iz2 + -2z + -4z2 = -8 + 4i Z3 + 12iz + -4iz2 + -2z + -4z2 = -8 + 4i Add '-12iz' to each side of the equation. Z3 + 12iz + -4iz2 + -2z + -12iz + -4z2 = -8 + 4i + -12iz Reorder the terms: Z3 + 12iz + -12iz + -4iz2 + -2z + -4z2 = -8 + 4i + -12iz Combine like terms: 12iz + -12iz = 0 Z3 + 0 + -4iz2 + -2z + -4z2 = -8 + 4i + -12iz Z3 + -4iz2 + -2z + -4z2 = -8 + 4i + -12iz Add '4iz2' to each side of the equation. Z3 + -4iz2 + -2z + 4iz2 + -4z2 = -8 + 4i + -12iz + 4iz2 Reorder the terms: Z3 + -4iz2 + 4iz2 + -2z + -4z2 = -8 + 4i + -12iz + 4iz2 Combine like terms: -4iz2 + 4iz2 = 0 Z3 + 0 + -2z + -4z2 = -8 + 4i + -12iz + 4iz2 Z3 + -2z + -4z2 = -8 + 4i + -12iz + 4iz2 Add '2z' to each side of the equation. Z3 + -2z + 2z + -4z2 = -8 + 4i + -12iz + 4iz2 + 2z Combine like terms: -2z + 2z = 0 Z3 + 0 + -4z2 = -8 + 4i + -12iz + 4iz2 + 2z Z3 + -4z2 = -8 + 4i + -12iz + 4iz2 + 2z Add '4z2' to each side of the equation. Z3 + -4z2 + 4z2 = -8 + 4i + -12iz + 4iz2 + 2z + 4z2 Combine like terms: -4z2 + 4z2 = 0 Z3 + 0 = -8 + 4i + -12iz + 4iz2 + 2z + 4z2 Z3 = -8 + 4i + -12iz + 4iz2 + 2z + 4z2 Simplifying Z3 = -8 + 4i + -12iz + 4iz2 + 2z + 4z2 Reorder the terms: 8 + Z3 + -4i + 12iz + -4iz2 + -2z + -4z2 = -8 + 4i + -12iz + 4iz2 + 2z + 4z2 + 8 + -4i + 12iz + -4iz2 + -2z + -4z2 Reorder the terms: 8 + Z3 + -4i + 12iz + -4iz2 + -2z + -4z2 = -8 + 8 + 4i + -4i + -12iz + 12iz + 4iz2 + -4iz2 + 2z + -2z + 4z2 + -4z2 Combine like terms: -8 + 8 = 0 8 + Z3 + -4i + 12iz + -4iz2 + -2z + -4z2 = 0 + 4i + -4i + -12iz + 12iz + 4iz2 + -4iz2 + 2z + -2z + 4z2 + -4z2 8 + Z3 + -4i + 12iz + -4iz2 + -2z + -4z2 = 4i + -4i + -12iz + 12iz + 4iz2 + -4iz2 + 2z + -2z + 4z2 + -4z2 Combine like terms: 4i + -4i = 0 8 + Z3 + -4i + 12iz + -4iz2 + -2z + -4z2 = 0 + -12iz + 12iz + 4iz2 + -4iz2 + 2z + -2z + 4z2 + -4z2 8 + Z3 + -4i + 12iz + -4iz2 + -2z + -4z2 = -12iz + 12iz + 4iz2 + -4iz2 + 2z + -2z + 4z2 + -4z2 Combine like terms: -12iz + 12iz = 0 8 + Z3 + -4i + 12iz + -4iz2 + -2z + -4z2 = 0 + 4iz2 + -4iz2 + 2z + -2z + 4z2 + -4z2 8 + Z3 + -4i + 12iz + -4iz2 + -2z + -4z2 = 4iz2 + -4iz2 + 2z + -2z + 4z2 + -4z2 Combine like terms: 4iz2 + -4iz2 = 0 8 + Z3 + -4i + 12iz + -4iz2 + -2z + -4z2 = 0 + 2z + -2z + 4z2 + -4z2 8 + Z3 + -4i + 12iz + -4iz2 + -2z + -4z2 = 2z + -2z + 4z2 + -4z2 Combine like terms: 2z + -2z = 0 8 + Z3 + -4i + 12iz + -4iz2 + -2z + -4z2 = 0 + 4z2 + -4z2 8 + Z3 + -4i + 12iz + -4iz2 + -2z + -4z2 = 4z2 + -4z2 Combine like terms: 4z2 + -4z2 = 0 8 + Z3 + -4i + 12iz + -4iz2 + -2z + -4z2 = 0 The solution to this equation could not be determined.
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