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