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Simplifying 2(x + yi) + 3(4 + -6i) = 7 + -3i Reorder the terms: 2(iy + x) + 3(4 + -6i) = 7 + -3i (iy * 2 + x * 2) + 3(4 + -6i) = 7 + -3i (2iy + 2x) + 3(4 + -6i) = 7 + -3i 2iy + 2x + (4 * 3 + -6i * 3) = 7 + -3i 2iy + 2x + (12 + -18i) = 7 + -3i Reorder the terms: 12 + -18i + 2iy + 2x = 7 + -3i Solving 12 + -18i + 2iy + 2x = 7 + -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. 12 + -18i + 2iy + 3i + 2x = 7 + -3i + 3i Reorder the terms: 12 + -18i + 3i + 2iy + 2x = 7 + -3i + 3i Combine like terms: -18i + 3i = -15i 12 + -15i + 2iy + 2x = 7 + -3i + 3i Combine like terms: -3i + 3i = 0 12 + -15i + 2iy + 2x = 7 + 0 12 + -15i + 2iy + 2x = 7 Add '-12' to each side of the equation. 12 + -15i + 2iy + -12 + 2x = 7 + -12 Reorder the terms: 12 + -12 + -15i + 2iy + 2x = 7 + -12 Combine like terms: 12 + -12 = 0 0 + -15i + 2iy + 2x = 7 + -12 -15i + 2iy + 2x = 7 + -12 Combine like terms: 7 + -12 = -5 -15i + 2iy + 2x = -5 Add '-2x' to each side of the equation. -15i + 2iy + 2x + -2x = -5 + -2x Combine like terms: 2x + -2x = 0 -15i + 2iy + 0 = -5 + -2x -15i + 2iy = -5 + -2x Reorder the terms: 5 + -15i + 2iy + 2x = -5 + -2x + 5 + 2x Reorder the terms: 5 + -15i + 2iy + 2x = -5 + 5 + -2x + 2x Combine like terms: -5 + 5 = 0 5 + -15i + 2iy + 2x = 0 + -2x + 2x 5 + -15i + 2iy + 2x = -2x + 2x Combine like terms: -2x + 2x = 0 5 + -15i + 2iy + 2x = 0 The solution to this equation could not be determined.
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