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Simplifying z2 + 2z + (1 + -8i) = 0 Remove parenthesis around (1 + -8i) z2 + 2z + 1 + -8i = 0 Reorder the terms: 1 + -8i + 2z + z2 = 0 Solving 1 + -8i + 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 + -8i + 2z + -1 + z2 = 0 + -1 Reorder the terms: 1 + -1 + -8i + 2z + z2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -8i + 2z + z2 = 0 + -1 -8i + 2z + z2 = 0 + -1 Combine like terms: 0 + -1 = -1 -8i + 2z + z2 = -1 Add '-2z' to each side of the equation. -8i + 2z + -2z + z2 = -1 + -2z Combine like terms: 2z + -2z = 0 -8i + 0 + z2 = -1 + -2z -8i + z2 = -1 + -2z Add '-1z2' to each side of the equation. -8i + z2 + -1z2 = -1 + -2z + -1z2 Combine like terms: z2 + -1z2 = 0 -8i + 0 = -1 + -2z + -1z2 -8i = -1 + -2z + -1z2 Divide each side by '-8'. i = 0.125 + 0.25z + 0.125z2 Simplifying i = 0.125 + 0.25z + 0.125z2
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