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