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Simplifying z2 + 2z + 2 + -1i = 0 Reorder the terms: 2 + -1i + 2z + z2 = 0 Solving 2 + -1i + 2z + z2 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -1i + 2z + -2 + z2 = 0 + -2 Reorder the terms: 2 + -2 + -1i + 2z + z2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1i + 2z + z2 = 0 + -2 -1i + 2z + z2 = 0 + -2 Combine like terms: 0 + -2 = -2 -1i + 2z + z2 = -2 Add '-2z' to each side of the equation. -1i + 2z + -2z + z2 = -2 + -2z Combine like terms: 2z + -2z = 0 -1i + 0 + z2 = -2 + -2z -1i + z2 = -2 + -2z Add '-1z2' to each side of the equation. -1i + z2 + -1z2 = -2 + -2z + -1z2 Combine like terms: z2 + -1z2 = 0 -1i + 0 = -2 + -2z + -1z2 -1i = -2 + -2z + -1z2 Divide each side by '-1'. i = 2 + 2z + z2 Simplifying i = 2 + 2z + z2
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