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Simplifying (5 + -1i) * z + (3 + 2i) = 8 + 3i Reorder the terms for easier multiplication: z(5 + -1i) + (3 + 2i) = 8 + 3i (5 * z + -1i * z) + (3 + 2i) = 8 + 3i Reorder the terms: (-1iz + 5z) + (3 + 2i) = 8 + 3i (-1iz + 5z) + (3 + 2i) = 8 + 3i Remove parenthesis around (3 + 2i) -1iz + 5z + 3 + 2i = 8 + 3i Reorder the terms: 3 + 2i + -1iz + 5z = 8 + 3i Solving 3 + 2i + -1iz + 5z = 8 + 3i Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-3i' to each side of the equation. 3 + 2i + -1iz + -3i + 5z = 8 + 3i + -3i Reorder the terms: 3 + 2i + -3i + -1iz + 5z = 8 + 3i + -3i Combine like terms: 2i + -3i = -1i 3 + -1i + -1iz + 5z = 8 + 3i + -3i Combine like terms: 3i + -3i = 0 3 + -1i + -1iz + 5z = 8 + 0 3 + -1i + -1iz + 5z = 8 Add '-3' to each side of the equation. 3 + -1i + -1iz + -3 + 5z = 8 + -3 Reorder the terms: 3 + -3 + -1i + -1iz + 5z = 8 + -3 Combine like terms: 3 + -3 = 0 0 + -1i + -1iz + 5z = 8 + -3 -1i + -1iz + 5z = 8 + -3 Combine like terms: 8 + -3 = 5 -1i + -1iz + 5z = 5 Add '-5z' to each side of the equation. -1i + -1iz + 5z + -5z = 5 + -5z Combine like terms: 5z + -5z = 0 -1i + -1iz + 0 = 5 + -5z -1i + -1iz = 5 + -5z Reorder the terms: -5 + -1i + -1iz + 5z = 5 + -5z + -5 + 5z Reorder the terms: -5 + -1i + -1iz + 5z = 5 + -5 + -5z + 5z Combine like terms: 5 + -5 = 0 -5 + -1i + -1iz + 5z = 0 + -5z + 5z -5 + -1i + -1iz + 5z = -5z + 5z Combine like terms: -5z + 5z = 0 -5 + -1i + -1iz + 5z = 0 The solution to this equation could not be determined.
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