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