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