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