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Simplifying (5 + 4i) + -1(x + yi) = (-1 + -3i) Remove parenthesis around (5 + 4i) 5 + 4i + -1(x + yi) = (-1 + -3i) Reorder the terms: 5 + 4i + -1(iy + x) = (-1 + -3i) 5 + 4i + (iy * -1 + x * -1) = (-1 + -3i) 5 + 4i + (-1iy + -1x) = (-1 + -3i) Remove parenthesis around (-1 + -3i) 5 + 4i + -1iy + -1x = -1 + -3i Solving 5 + 4i + -1iy + -1x = -1 + -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. 5 + 4i + -1iy + 3i + -1x = -1 + -3i + 3i Reorder the terms: 5 + 4i + 3i + -1iy + -1x = -1 + -3i + 3i Combine like terms: 4i + 3i = 7i 5 + 7i + -1iy + -1x = -1 + -3i + 3i Combine like terms: -3i + 3i = 0 5 + 7i + -1iy + -1x = -1 + 0 5 + 7i + -1iy + -1x = -1 Add '-5' to each side of the equation. 5 + 7i + -1iy + -5 + -1x = -1 + -5 Reorder the terms: 5 + -5 + 7i + -1iy + -1x = -1 + -5 Combine like terms: 5 + -5 = 0 0 + 7i + -1iy + -1x = -1 + -5 7i + -1iy + -1x = -1 + -5 Combine like terms: -1 + -5 = -6 7i + -1iy + -1x = -6 Add 'x' to each side of the equation. 7i + -1iy + -1x + x = -6 + x Combine like terms: -1x + x = 0 7i + -1iy + 0 = -6 + x 7i + -1iy = -6 + x Reorder the terms: 6 + 7i + -1iy + -1x = -6 + x + 6 + -1x Reorder the terms: 6 + 7i + -1iy + -1x = -6 + 6 + x + -1x Combine like terms: -6 + 6 = 0 6 + 7i + -1iy + -1x = 0 + x + -1x 6 + 7i + -1iy + -1x = x + -1x Combine like terms: x + -1x = 0 6 + 7i + -1iy + -1x = 0 The solution to this equation could not be determined.
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