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Simplifying (z + -1i) * z + 8z = 0 Reorder the terms: (-1i + z) * z + 8z = 0 Reorder the terms for easier multiplication: z(-1i + z) + 8z = 0 (-1i * z + z * z) + 8z = 0 (-1iz + z2) + 8z = 0 Reorder the terms: -1iz + 8z + z2 = 0 Solving -1iz + 8z + z2 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-8z' to each side of the equation. -1iz + 8z + -8z + z2 = 0 + -8z Combine like terms: 8z + -8z = 0 -1iz + 0 + z2 = 0 + -8z -1iz + z2 = 0 + -8z Remove the zero: -1iz + z2 = -8z Add '-1z2' to each side of the equation. -1iz + z2 + -1z2 = -8z + -1z2 Combine like terms: z2 + -1z2 = 0 -1iz + 0 = -8z + -1z2 -1iz = -8z + -1z2 Divide each side by '-1z'. i = 8 + z Simplifying i = 8 + z
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