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Simplifying z2 + (5 + -2i) * z + 5 + -5 = 0i Reorder the terms for easier multiplication: z2 + z(5 + -2i) + 5 + -5 = 0i z2 + (5 * z + -2i * z) + 5 + -5 = 0i Reorder the terms: z2 + (-2iz + 5z) + 5 + -5 = 0i z2 + (-2iz + 5z) + 5 + -5 = 0i Reorder the terms: 5 + -5 + -2iz + 5z + z2 = 0i Combine like terms: 5 + -5 = 0 0 + -2iz + 5z + z2 = 0i -2iz + 5z + z2 = 0i Anything times zero is zero. -2iz + 5z + z2 = 0i Solving -2iz + 5z + z2 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-5z' to each side of the equation. -2iz + 5z + -5z + z2 = 0 + -5z Combine like terms: 5z + -5z = 0 -2iz + 0 + z2 = 0 + -5z -2iz + z2 = 0 + -5z Remove the zero: -2iz + z2 = -5z Add '-1z2' to each side of the equation. -2iz + z2 + -1z2 = -5z + -1z2 Combine like terms: z2 + -1z2 = 0 -2iz + 0 = -5z + -1z2 -2iz = -5z + -1z2 Divide each side by '-2z'. i = 2.5 + 0.5z Simplifying i = 2.5 + 0.5z
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