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Simplifying (1 + -2i) * z + 3 + 5i = 5 + -4i Reorder the terms for easier multiplication: z(1 + -2i) + 3 + 5i = 5 + -4i (1 * z + -2i * z) + 3 + 5i = 5 + -4i Reorder the terms: (-2iz + 1z) + 3 + 5i = 5 + -4i (-2iz + 1z) + 3 + 5i = 5 + -4i Reorder the terms: 3 + 5i + -2iz + 1z = 5 + -4i Solving 3 + 5i + -2iz + 1z = 5 + -4i Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '4i' to each side of the equation. 3 + 5i + -2iz + 4i + 1z = 5 + -4i + 4i Reorder the terms: 3 + 5i + 4i + -2iz + 1z = 5 + -4i + 4i Combine like terms: 5i + 4i = 9i 3 + 9i + -2iz + 1z = 5 + -4i + 4i Combine like terms: -4i + 4i = 0 3 + 9i + -2iz + 1z = 5 + 0 3 + 9i + -2iz + 1z = 5 Add '-3' to each side of the equation. 3 + 9i + -2iz + -3 + 1z = 5 + -3 Reorder the terms: 3 + -3 + 9i + -2iz + 1z = 5 + -3 Combine like terms: 3 + -3 = 0 0 + 9i + -2iz + 1z = 5 + -3 9i + -2iz + 1z = 5 + -3 Combine like terms: 5 + -3 = 2 9i + -2iz + 1z = 2 Add '-1z' to each side of the equation. 9i + -2iz + 1z + -1z = 2 + -1z Combine like terms: 1z + -1z = 0 9i + -2iz + 0 = 2 + -1z 9i + -2iz = 2 + -1z Reorder the terms: -2 + 9i + -2iz + z = 2 + -1z + -2 + z Reorder the terms: -2 + 9i + -2iz + z = 2 + -2 + -1z + z Combine like terms: 2 + -2 = 0 -2 + 9i + -2iz + z = 0 + -1z + z -2 + 9i + -2iz + z = -1z + z Combine like terms: -1z + z = 0 -2 + 9i + -2iz + z = 0 The solution to this equation could not be determined.
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