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