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Simplifying (x + 3i) = (4 + -1i) + (5 + -4yi) Reorder the terms: (3i + x) = (4 + -1i) + (5 + -4yi) Remove parenthesis around (3i + x) 3i + x = (4 + -1i) + (5 + -4yi) Remove parenthesis around (4 + -1i) 3i + x = 4 + -1i + (5 + -4yi) Remove parenthesis around (5 + -4iy) 3i + x = 4 + -1i + 5 + -4iy Reorder the terms: 3i + x = 4 + 5 + -1i + -4iy Combine like terms: 4 + 5 = 9 3i + x = 9 + -1i + -4iy Solving 3i + x = 9 + -1i + -4iy Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add 'i' to each side of the equation. 3i + i + x = 9 + -1i + i + -4iy Combine like terms: 3i + i = 4i 4i + x = 9 + -1i + i + -4iy Combine like terms: -1i + i = 0 4i + x = 9 + 0 + -4iy 4i + x = 9 + -4iy Add '4iy' to each side of the equation. 4i + 4iy + x = 9 + -4iy + 4iy Combine like terms: -4iy + 4iy = 0 4i + 4iy + x = 9 + 0 4i + 4iy + x = 9 Add '-1x' to each side of the equation. 4i + 4iy + x + -1x = 9 + -1x Combine like terms: x + -1x = 0 4i + 4iy + 0 = 9 + -1x 4i + 4iy = 9 + -1x Reorder the terms: -9 + 4i + 4iy + x = 9 + -1x + -9 + x Reorder the terms: -9 + 4i + 4iy + x = 9 + -9 + -1x + x Combine like terms: 9 + -9 = 0 -9 + 4i + 4iy + x = 0 + -1x + x -9 + 4i + 4iy + x = -1x + x Combine like terms: -1x + x = 0 -9 + 4i + 4iy + x = 0 The solution to this equation could not be determined.
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