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Simplifying z3 + -1z + 1 + -8i = 0 Reorder the terms: 1 + -8i + -1z + z3 = 0 Solving 1 + -8i + -1z + z3 = 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 + -8i + -1z + -1 + z3 = 0 + -1 Reorder the terms: 1 + -1 + -8i + -1z + z3 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -8i + -1z + z3 = 0 + -1 -8i + -1z + z3 = 0 + -1 Combine like terms: 0 + -1 = -1 -8i + -1z + z3 = -1 Add 'z' to each side of the equation. -8i + -1z + z + z3 = -1 + z Combine like terms: -1z + z = 0 -8i + 0 + z3 = -1 + z -8i + z3 = -1 + z Add '-1z3' to each side of the equation. -8i + z3 + -1z3 = -1 + z + -1z3 Combine like terms: z3 + -1z3 = 0 -8i + 0 = -1 + z + -1z3 -8i = -1 + z + -1z3 Divide each side by '-8'. i = 0.125 + -0.125z + 0.125z3 Simplifying i = 0.125 + -0.125z + 0.125z3
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