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Simplifying (1 + i) * z + 2 + -3i = 3 + i Reorder the terms for easier multiplication: z(1 + i) + 2 + -3i = 3 + i (1 * z + i * z) + 2 + -3i = 3 + i Reorder the terms: (iz + 1z) + 2 + -3i = 3 + i (iz + 1z) + 2 + -3i = 3 + i Reorder the terms: 2 + -3i + iz + 1z = 3 + i Solving 2 + -3i + iz + 1z = 3 + i Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-1i' to each side of the equation. 2 + -3i + iz + -1i + 1z = 3 + i + -1i Reorder the terms: 2 + -3i + -1i + iz + 1z = 3 + i + -1i Combine like terms: -3i + -1i = -4i 2 + -4i + iz + 1z = 3 + i + -1i Combine like terms: i + -1i = 0 2 + -4i + iz + 1z = 3 + 0 2 + -4i + iz + 1z = 3 Add '-2' to each side of the equation. 2 + -4i + iz + -2 + 1z = 3 + -2 Reorder the terms: 2 + -2 + -4i + iz + 1z = 3 + -2 Combine like terms: 2 + -2 = 0 0 + -4i + iz + 1z = 3 + -2 -4i + iz + 1z = 3 + -2 Combine like terms: 3 + -2 = 1 -4i + iz + 1z = 1 Add '-1z' to each side of the equation. -4i + iz + 1z + -1z = 1 + -1z Combine like terms: 1z + -1z = 0 -4i + iz + 0 = 1 + -1z -4i + iz = 1 + -1z Reorder the terms: -1 + -4i + iz + z = 1 + -1z + -1 + z Reorder the terms: -1 + -4i + iz + z = 1 + -1 + -1z + z Combine like terms: 1 + -1 = 0 -1 + -4i + iz + z = 0 + -1z + z -1 + -4i + iz + z = -1z + z Combine like terms: -1z + z = 0 -1 + -4i + iz + z = 0 The solution to this equation could not be determined.
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