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Simplifying 4x + y + 9i = -4 + -1y + 12xi + 3yi Reorder the terms: 9i + 4x + y = -4 + -1y + 12xi + 3yi Reorder the terms: 9i + 4x + y = -4 + 12ix + 3iy + -1y Solving 9i + 4x + y = -4 + 12ix + 3iy + -1y Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-12ix' to each side of the equation. 9i + 4x + -12ix + y = -4 + 12ix + 3iy + -12ix + -1y Reorder the terms: 9i + -12ix + 4x + y = -4 + 12ix + 3iy + -12ix + -1y Reorder the terms: 9i + -12ix + 4x + y = -4 + 12ix + -12ix + 3iy + -1y Combine like terms: 12ix + -12ix = 0 9i + -12ix + 4x + y = -4 + 0 + 3iy + -1y 9i + -12ix + 4x + y = -4 + 3iy + -1y Add '-3iy' to each side of the equation. 9i + -12ix + 4x + -3iy + y = -4 + 3iy + -3iy + -1y Reorder the terms: 9i + -12ix + -3iy + 4x + y = -4 + 3iy + -3iy + -1y Combine like terms: 3iy + -3iy = 0 9i + -12ix + -3iy + 4x + y = -4 + 0 + -1y 9i + -12ix + -3iy + 4x + y = -4 + -1y Add '-4x' to each side of the equation. 9i + -12ix + -3iy + 4x + -4x + y = -4 + -4x + -1y Combine like terms: 4x + -4x = 0 9i + -12ix + -3iy + 0 + y = -4 + -4x + -1y 9i + -12ix + -3iy + y = -4 + -4x + -1y Add '-1y' to each side of the equation. 9i + -12ix + -3iy + y + -1y = -4 + -4x + -1y + -1y Combine like terms: y + -1y = 0 9i + -12ix + -3iy + 0 = -4 + -4x + -1y + -1y 9i + -12ix + -3iy = -4 + -4x + -1y + -1y Combine like terms: -1y + -1y = -2y 9i + -12ix + -3iy = -4 + -4x + -2y Reorder the terms: 4 + 9i + -12ix + -3iy + 4x + 2y = -4 + -4x + -2y + 4 + 4x + 2y Reorder the terms: 4 + 9i + -12ix + -3iy + 4x + 2y = -4 + 4 + -4x + 4x + -2y + 2y Combine like terms: -4 + 4 = 0 4 + 9i + -12ix + -3iy + 4x + 2y = 0 + -4x + 4x + -2y + 2y 4 + 9i + -12ix + -3iy + 4x + 2y = -4x + 4x + -2y + 2y Combine like terms: -4x + 4x = 0 4 + 9i + -12ix + -3iy + 4x + 2y = 0 + -2y + 2y 4 + 9i + -12ix + -3iy + 4x + 2y = -2y + 2y Combine like terms: -2y + 2y = 0 4 + 9i + -12ix + -3iy + 4x + 2y = 0 The solution to this equation could not be determined.
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