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Simplifying z2 + 4z + 4 + 8i = 0 Reorder the terms: 4 + 8i + 4z + z2 = 0 Solving 4 + 8i + 4z + z2 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + 8i + 4z + -4 + z2 = 0 + -4 Reorder the terms: 4 + -4 + 8i + 4z + z2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 8i + 4z + z2 = 0 + -4 8i + 4z + z2 = 0 + -4 Combine like terms: 0 + -4 = -4 8i + 4z + z2 = -4 Add '-4z' to each side of the equation. 8i + 4z + -4z + z2 = -4 + -4z Combine like terms: 4z + -4z = 0 8i + 0 + z2 = -4 + -4z 8i + z2 = -4 + -4z Add '-1z2' to each side of the equation. 8i + z2 + -1z2 = -4 + -4z + -1z2 Combine like terms: z2 + -1z2 = 0 8i + 0 = -4 + -4z + -1z2 8i = -4 + -4z + -1z2 Divide each side by '8'. i = -0.5 + -0.5z + -0.125z2 Simplifying i = -0.5 + -0.5z + -0.125z2
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