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Simplifying z3 + i * z2 + 3z + 9 = 0 Multiply i * z2 z3 + iz2 + 3z + 9 = 0 Reorder the terms: 9 + iz2 + 3z + z3 = 0 Solving 9 + iz2 + 3z + z3 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + iz2 + 3z + -9 + z3 = 0 + -9 Reorder the terms: 9 + -9 + iz2 + 3z + z3 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + iz2 + 3z + z3 = 0 + -9 iz2 + 3z + z3 = 0 + -9 Combine like terms: 0 + -9 = -9 iz2 + 3z + z3 = -9 Add '-3z' to each side of the equation. iz2 + 3z + -3z + z3 = -9 + -3z Combine like terms: 3z + -3z = 0 iz2 + 0 + z3 = -9 + -3z iz2 + z3 = -9 + -3z Add '-1z3' to each side of the equation. iz2 + z3 + -1z3 = -9 + -3z + -1z3 Combine like terms: z3 + -1z3 = 0 iz2 + 0 = -9 + -3z + -1z3 iz2 = -9 + -3z + -1z3 Divide each side by 'z2'. i = -9z-2 + -3z-1 + -1z Simplifying i = -9z-2 + -3z-1 + -1z
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