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Simplifying z2 + 3z + 1 + -2i = 0 Reorder the terms: 1 + -2i + 3z + z2 = 0 Solving 1 + -2i + 3z + z2 = 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 + -2i + 3z + -1 + z2 = 0 + -1 Reorder the terms: 1 + -1 + -2i + 3z + z2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2i + 3z + z2 = 0 + -1 -2i + 3z + z2 = 0 + -1 Combine like terms: 0 + -1 = -1 -2i + 3z + z2 = -1 Add '-3z' to each side of the equation. -2i + 3z + -3z + z2 = -1 + -3z Combine like terms: 3z + -3z = 0 -2i + 0 + z2 = -1 + -3z -2i + z2 = -1 + -3z Add '-1z2' to each side of the equation. -2i + z2 + -1z2 = -1 + -3z + -1z2 Combine like terms: z2 + -1z2 = 0 -2i + 0 = -1 + -3z + -1z2 -2i = -1 + -3z + -1z2 Divide each side by '-2'. i = 0.5 + 1.5z + 0.5z2 Simplifying i = 0.5 + 1.5z + 0.5z2
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