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Simplifying (2 + -1i) * z + (1 + -4i) = (-1 + 3i) * z + (4 + 2i) Reorder the terms for easier multiplication: z(2 + -1i) + (1 + -4i) = (-1 + 3i) * z + (4 + 2i) (2 * z + -1i * z) + (1 + -4i) = (-1 + 3i) * z + (4 + 2i) Reorder the terms: (-1iz + 2z) + (1 + -4i) = (-1 + 3i) * z + (4 + 2i) (-1iz + 2z) + (1 + -4i) = (-1 + 3i) * z + (4 + 2i) Remove parenthesis around (1 + -4i) -1iz + 2z + 1 + -4i = (-1 + 3i) * z + (4 + 2i) Reorder the terms: 1 + -4i + -1iz + 2z = (-1 + 3i) * z + (4 + 2i) Reorder the terms for easier multiplication: 1 + -4i + -1iz + 2z = z(-1 + 3i) + (4 + 2i) 1 + -4i + -1iz + 2z = (-1 * z + 3i * z) + (4 + 2i) Reorder the terms: 1 + -4i + -1iz + 2z = (3iz + -1z) + (4 + 2i) 1 + -4i + -1iz + 2z = (3iz + -1z) + (4 + 2i) Remove parenthesis around (4 + 2i) 1 + -4i + -1iz + 2z = 3iz + -1z + 4 + 2i Reorder the terms: 1 + -4i + -1iz + 2z = 4 + 2i + 3iz + -1z Solving 1 + -4i + -1iz + 2z = 4 + 2i + 3iz + -1z Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-2i' to each side of the equation. 1 + -4i + -1iz + -2i + 2z = 4 + 2i + 3iz + -2i + -1z Reorder the terms: 1 + -4i + -2i + -1iz + 2z = 4 + 2i + 3iz + -2i + -1z Combine like terms: -4i + -2i = -6i 1 + -6i + -1iz + 2z = 4 + 2i + 3iz + -2i + -1z Reorder the terms: 1 + -6i + -1iz + 2z = 4 + 2i + -2i + 3iz + -1z Combine like terms: 2i + -2i = 0 1 + -6i + -1iz + 2z = 4 + 0 + 3iz + -1z 1 + -6i + -1iz + 2z = 4 + 3iz + -1z Add '-3iz' to each side of the equation. 1 + -6i + -1iz + -3iz + 2z = 4 + 3iz + -3iz + -1z Combine like terms: -1iz + -3iz = -4iz 1 + -6i + -4iz + 2z = 4 + 3iz + -3iz + -1z Combine like terms: 3iz + -3iz = 0 1 + -6i + -4iz + 2z = 4 + 0 + -1z 1 + -6i + -4iz + 2z = 4 + -1z Add '-1' to each side of the equation. 1 + -6i + -4iz + -1 + 2z = 4 + -1 + -1z Reorder the terms: 1 + -1 + -6i + -4iz + 2z = 4 + -1 + -1z Combine like terms: 1 + -1 = 0 0 + -6i + -4iz + 2z = 4 + -1 + -1z -6i + -4iz + 2z = 4 + -1 + -1z Combine like terms: 4 + -1 = 3 -6i + -4iz + 2z = 3 + -1z Add '-2z' to each side of the equation. -6i + -4iz + 2z + -2z = 3 + -1z + -2z Combine like terms: 2z + -2z = 0 -6i + -4iz + 0 = 3 + -1z + -2z -6i + -4iz = 3 + -1z + -2z Combine like terms: -1z + -2z = -3z -6i + -4iz = 3 + -3z Reorder the terms: -3 + -6i + -4iz + 3z = 3 + -3z + -3 + 3z Reorder the terms: -3 + -6i + -4iz + 3z = 3 + -3 + -3z + 3z Combine like terms: 3 + -3 = 0 -3 + -6i + -4iz + 3z = 0 + -3z + 3z -3 + -6i + -4iz + 3z = -3z + 3z Combine like terms: -3z + 3z = 0 -3 + -6i + -4iz + 3z = 0 The solution to this equation could not be determined.
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