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Simplifying z2 + (1 + 4i) * z + -1(5 + i) = 0 Reorder the terms for easier multiplication: z2 + z(1 + 4i) + -1(5 + i) = 0 z2 + (1 * z + 4i * z) + -1(5 + i) = 0 Reorder the terms: z2 + (4iz + 1z) + -1(5 + i) = 0 z2 + (4iz + 1z) + -1(5 + i) = 0 z2 + 4iz + 1z + (5 * -1 + i * -1) = 0 z2 + 4iz + 1z + (-5 + -1i) = 0 Reorder the terms: -5 + -1i + 4iz + 1z + z2 = 0 Solving -5 + -1i + 4iz + 1z + z2 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '5' to each side of the equation. -5 + -1i + 4iz + 1z + 5 + z2 = 0 + 5 Reorder the terms: -5 + 5 + -1i + 4iz + 1z + z2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1i + 4iz + 1z + z2 = 0 + 5 -1i + 4iz + 1z + z2 = 0 + 5 Combine like terms: 0 + 5 = 5 -1i + 4iz + 1z + z2 = 5 Add '-1z' to each side of the equation. -1i + 4iz + 1z + -1z + z2 = 5 + -1z Combine like terms: 1z + -1z = 0 -1i + 4iz + 0 + z2 = 5 + -1z -1i + 4iz + z2 = 5 + -1z Add '-1z2' to each side of the equation. -1i + 4iz + z2 + -1z2 = 5 + -1z + -1z2 Combine like terms: z2 + -1z2 = 0 -1i + 4iz + 0 = 5 + -1z + -1z2 -1i + 4iz = 5 + -1z + -1z2 Reorder the terms: -5 + -1i + 4iz + z + z2 = 5 + -1z + -1z2 + -5 + z + z2 Reorder the terms: -5 + -1i + 4iz + z + z2 = 5 + -5 + -1z + z + -1z2 + z2 Combine like terms: 5 + -5 = 0 -5 + -1i + 4iz + z + z2 = 0 + -1z + z + -1z2 + z2 -5 + -1i + 4iz + z + z2 = -1z + z + -1z2 + z2 Combine like terms: -1z + z = 0 -5 + -1i + 4iz + z + z2 = 0 + -1z2 + z2 -5 + -1i + 4iz + z + z2 = -1z2 + z2 Combine like terms: -1z2 + z2 = 0 -5 + -1i + 4iz + z + z2 = 0 The solution to this equation could not be determined.
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