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Simplifying (2x + 3yi) + -1(5 + 2i) = (x + -12i) + (x + -4i) Reorder the terms: (3iy + 2x) + -1(5 + 2i) = (x + -12i) + (x + -4i) Remove parenthesis around (3iy + 2x) 3iy + 2x + -1(5 + 2i) = (x + -12i) + (x + -4i) 3iy + 2x + (5 * -1 + 2i * -1) = (x + -12i) + (x + -4i) 3iy + 2x + (-5 + -2i) = (x + -12i) + (x + -4i) Reorder the terms: -5 + -2i + 3iy + 2x = (x + -12i) + (x + -4i) Reorder the terms: -5 + -2i + 3iy + 2x = (-12i + x) + (x + -4i) Remove parenthesis around (-12i + x) -5 + -2i + 3iy + 2x = -12i + x + (x + -4i) Reorder the terms: -5 + -2i + 3iy + 2x = -12i + x + (-4i + x) Remove parenthesis around (-4i + x) -5 + -2i + 3iy + 2x = -12i + x + -4i + x Reorder the terms: -5 + -2i + 3iy + 2x = -12i + -4i + x + x Combine like terms: -12i + -4i = -16i -5 + -2i + 3iy + 2x = -16i + x + x Combine like terms: x + x = 2x -5 + -2i + 3iy + 2x = -16i + 2x Add '-2x' to each side of the equation. -5 + -2i + 3iy + 2x + -2x = -16i + 2x + -2x Combine like terms: 2x + -2x = 0 -5 + -2i + 3iy + 0 = -16i + 2x + -2x -5 + -2i + 3iy = -16i + 2x + -2x Combine like terms: 2x + -2x = 0 -5 + -2i + 3iy = -16i + 0 -5 + -2i + 3iy = -16i Solving -5 + -2i + 3iy = -16i Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '16i' to each side of the equation. -5 + -2i + 16i + 3iy = -16i + 16i Combine like terms: -2i + 16i = 14i -5 + 14i + 3iy = -16i + 16i Combine like terms: -16i + 16i = 0 -5 + 14i + 3iy = 0 Add '5' to each side of the equation. -5 + 14i + 5 + 3iy = 0 + 5 Reorder the terms: -5 + 5 + 14i + 3iy = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 14i + 3iy = 0 + 5 14i + 3iy = 0 + 5 Combine like terms: 0 + 5 = 5 14i + 3iy = 5 Reorder the terms: -5 + 14i + 3iy = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + 14i + 3iy = 0 The solution to this equation could not be determined.
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