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Simplifying y = [x + -1(1 + -1i)][x + -1(1 + i)] y = [x + (1 * -1 + -1i * -1)][x + -1(1 + i)] y = [x + (-1 + 1i)][x + -1(1 + i)] Reorder the terms: y = [-1 + 1i + x][x + -1(1 + i)] y = [-1 + 1i + x][x + (1 * -1 + i * -1)] y = [-1 + 1i + x][x + (-1 + -1i)] Reorder the terms: y = [-1 + 1i + x][-1 + -1i + x] Multiply [-1 + 1i + x] * [-1 + -1i + x] y = [-1[-1 + -1i + x] + 1i * [-1 + -1i + x] + x[-1 + -1i + x]] y = [[-1 * -1 + -1i * -1 + x * -1] + 1i * [-1 + -1i + x] + x[-1 + -1i + x]] y = [[1 + 1i + -1x] + 1i * [-1 + -1i + x] + x[-1 + -1i + x]] y = [1 + 1i + -1x + [-1 * 1i + -1i * 1i + x * 1i] + x[-1 + -1i + x]] Reorder the terms: y = [1 + 1i + -1x + [-1i + 1ix + -1i2] + x[-1 + -1i + x]] y = [1 + 1i + -1x + [-1i + 1ix + -1i2] + x[-1 + -1i + x]] y = [1 + 1i + -1x + -1i + 1ix + -1i2 + [-1 * x + -1i * x + x * x]] Reorder the terms: y = [1 + 1i + -1x + -1i + 1ix + -1i2 + [-1ix + -1x + x2]] y = [1 + 1i + -1x + -1i + 1ix + -1i2 + [-1ix + -1x + x2]] Reorder the terms: y = [1 + 1i + -1i + 1ix + -1ix + -1i2 + -1x + -1x + x2] Combine like terms: 1i + -1i = 0 y = [1 + 0 + 1ix + -1ix + -1i2 + -1x + -1x + x2] y = [1 + 1ix + -1ix + -1i2 + -1x + -1x + x2] Combine like terms: 1ix + -1ix = 0 y = [1 + 0 + -1i2 + -1x + -1x + x2] y = [1 + -1i2 + -1x + -1x + x2] Combine like terms: -1x + -1x = -2x y = [1 + -1i2 + -2x + x2] Solving y = 1 + -1i2 + -2x + x2 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Simplifying y = 1 + -1i2 + -2x + x2
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