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Simplifying z2 + 2(1 + -2i) * z + 2 = 0 Reorder the terms for easier multiplication: z2 + 2z(1 + -2i) + 2 = 0 z2 + (1 * 2z + -2i * 2z) + 2 = 0 Reorder the terms: z2 + (-4iz + 2z) + 2 = 0 z2 + (-4iz + 2z) + 2 = 0 Reorder the terms: 2 + -4iz + 2z + z2 = 0 Solving 2 + -4iz + 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 + -4iz + 2z + -2 + z2 = 0 + -2 Reorder the terms: 2 + -2 + -4iz + 2z + z2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -4iz + 2z + z2 = 0 + -2 -4iz + 2z + z2 = 0 + -2 Combine like terms: 0 + -2 = -2 -4iz + 2z + z2 = -2 Add '-2z' to each side of the equation. -4iz + 2z + -2z + z2 = -2 + -2z Combine like terms: 2z + -2z = 0 -4iz + 0 + z2 = -2 + -2z -4iz + z2 = -2 + -2z Add '-1z2' to each side of the equation. -4iz + z2 + -1z2 = -2 + -2z + -1z2 Combine like terms: z2 + -1z2 = 0 -4iz + 0 = -2 + -2z + -1z2 -4iz = -2 + -2z + -1z2 Divide each side by '-4z'. i = 0.5z-1 + 0.5 + 0.25z Simplifying i = 0.5z-1 + 0.5 + 0.25z Reorder the terms: i = 0.5 + 0.5z-1 + 0.25z
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