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