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Simplifying z2 + 6z + 9 + 2i = 0 Reorder the terms: 9 + 2i + 6z + z2 = 0 Solving 9 + 2i + 6z + z2 = 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 + 2i + 6z + -9 + z2 = 0 + -9 Reorder the terms: 9 + -9 + 2i + 6z + z2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 2i + 6z + z2 = 0 + -9 2i + 6z + z2 = 0 + -9 Combine like terms: 0 + -9 = -9 2i + 6z + z2 = -9 Add '-6z' to each side of the equation. 2i + 6z + -6z + z2 = -9 + -6z Combine like terms: 6z + -6z = 0 2i + 0 + z2 = -9 + -6z 2i + z2 = -9 + -6z Add '-1z2' to each side of the equation. 2i + z2 + -1z2 = -9 + -6z + -1z2 Combine like terms: z2 + -1z2 = 0 2i + 0 = -9 + -6z + -1z2 2i = -9 + -6z + -1z2 Divide each side by '2'. i = -4.5 + -3z + -0.5z2 Simplifying i = -4.5 + -3z + -0.5z2
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