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Simplifying z2 + z + -1 + -3i = 0 Reorder the terms: -1 + -3i + z + z2 = 0 Solving -1 + -3i + z + z2 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '1' to each side of the equation. -1 + -3i + z + 1 + z2 = 0 + 1 Reorder the terms: -1 + 1 + -3i + z + z2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -3i + z + z2 = 0 + 1 -3i + z + z2 = 0 + 1 Combine like terms: 0 + 1 = 1 -3i + z + z2 = 1 Add '-1z' to each side of the equation. -3i + z + -1z + z2 = 1 + -1z Combine like terms: z + -1z = 0 -3i + 0 + z2 = 1 + -1z -3i + z2 = 1 + -1z Add '-1z2' to each side of the equation. -3i + z2 + -1z2 = 1 + -1z + -1z2 Combine like terms: z2 + -1z2 = 0 -3i + 0 = 1 + -1z + -1z2 -3i = 1 + -1z + -1z2 Divide each side by '-3'. i = -0.3333333333 + 0.3333333333z + 0.3333333333z2 Simplifying i = -0.3333333333 + 0.3333333333z + 0.3333333333z2
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