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Simplifying (5 + 3i) * x + -1(2 + 5i) * y = 11 + -1i Reorder the terms for easier multiplication: x(5 + 3i) + -1(2 + 5i) * y = 11 + -1i (5 * x + 3i * x) + -1(2 + 5i) * y = 11 + -1i Reorder the terms: (3ix + 5x) + -1(2 + 5i) * y = 11 + -1i (3ix + 5x) + -1(2 + 5i) * y = 11 + -1i Reorder the terms for easier multiplication: 3ix + 5x + -1y(2 + 5i) = 11 + -1i 3ix + 5x + (2 * -1y + 5i * -1y) = 11 + -1i Reorder the terms: 3ix + 5x + (-5iy + -2y) = 11 + -1i 3ix + 5x + (-5iy + -2y) = 11 + -1i Reorder the terms: 3ix + -5iy + 5x + -2y = 11 + -1i Solving 3ix + -5iy + 5x + -2y = 11 + -1i 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. 3ix + -5iy + 5x + i + -2y = 11 + -1i + i Reorder the terms: i + 3ix + -5iy + 5x + -2y = 11 + -1i + i Combine like terms: -1i + i = 0 i + 3ix + -5iy + 5x + -2y = 11 + 0 i + 3ix + -5iy + 5x + -2y = 11 Add '-5x' to each side of the equation. i + 3ix + -5iy + 5x + -5x + -2y = 11 + -5x Combine like terms: 5x + -5x = 0 i + 3ix + -5iy + 0 + -2y = 11 + -5x i + 3ix + -5iy + -2y = 11 + -5x Add '2y' to each side of the equation. i + 3ix + -5iy + -2y + 2y = 11 + -5x + 2y Combine like terms: -2y + 2y = 0 i + 3ix + -5iy + 0 = 11 + -5x + 2y i + 3ix + -5iy = 11 + -5x + 2y Reorder the terms: -11 + i + 3ix + -5iy + 5x + -2y = 11 + -5x + 2y + -11 + 5x + -2y Reorder the terms: -11 + i + 3ix + -5iy + 5x + -2y = 11 + -11 + -5x + 5x + 2y + -2y Combine like terms: 11 + -11 = 0 -11 + i + 3ix + -5iy + 5x + -2y = 0 + -5x + 5x + 2y + -2y -11 + i + 3ix + -5iy + 5x + -2y = -5x + 5x + 2y + -2y Combine like terms: -5x + 5x = 0 -11 + i + 3ix + -5iy + 5x + -2y = 0 + 2y + -2y -11 + i + 3ix + -5iy + 5x + -2y = 2y + -2y Combine like terms: 2y + -2y = 0 -11 + i + 3ix + -5iy + 5x + -2y = 0 The solution to this equation could not be determined.
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