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