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Simplifying [x + -1(1 + i)][x + -1(1 + -1i)] = 0 [x + (1 * -1 + i * -1)][x + -1(1 + -1i)] = 0 [x + (-1 + -1i)][x + -1(1 + -1i)] = 0 Reorder the terms: [-1 + -1i + x][x + -1(1 + -1i)] = 0 [-1 + -1i + x][x + (1 * -1 + -1i * -1)] = 0 [-1 + -1i + x][x + (-1 + 1i)] = 0 Reorder the terms: [-1 + -1i + x][-1 + 1i + x] = 0 Multiply [-1 + -1i + x] * [-1 + 1i + x] [-1[-1 + 1i + x] + -1i * [-1 + 1i + x] + x[-1 + 1i + x]] = 0 [[-1 * -1 + 1i * -1 + x * -1] + -1i * [-1 + 1i + x] + x[-1 + 1i + x]] = 0 [[1 + -1i + -1x] + -1i * [-1 + 1i + x] + x[-1 + 1i + x]] = 0 [1 + -1i + -1x + [-1 * -1i + 1i * -1i + x * -1i] + x[-1 + 1i + x]] = 0 Reorder the terms: [1 + -1i + -1x + [1i + -1ix + -1i2] + x[-1 + 1i + x]] = 0 [1 + -1i + -1x + [1i + -1ix + -1i2] + x[-1 + 1i + x]] = 0 [1 + -1i + -1x + 1i + -1ix + -1i2 + [-1 * x + 1i * x + x * x]] = 0 Reorder the terms: [1 + -1i + -1x + 1i + -1ix + -1i2 + [1ix + -1x + x2]] = 0 [1 + -1i + -1x + 1i + -1ix + -1i2 + [1ix + -1x + x2]] = 0 Reorder the terms: [1 + -1i + 1i + -1ix + 1ix + -1i2 + -1x + -1x + x2] = 0 Combine like terms: -1i + 1i = 0 [1 + 0 + -1ix + 1ix + -1i2 + -1x + -1x + x2] = 0 [1 + -1ix + 1ix + -1i2 + -1x + -1x + x2] = 0 Combine like terms: -1ix + 1ix = 0 [1 + 0 + -1i2 + -1x + -1x + x2] = 0 [1 + -1i2 + -1x + -1x + x2] = 0 Combine like terms: -1x + -1x = -2x [1 + -1i2 + -2x + x2] = 0 Solving 1 + -1i2 + -2x + x2 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1i2 + -2x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + -1i2 + -2x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1i2 + -2x + x2 = 0 + -1 -1i2 + -2x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 -1i2 + -2x + x2 = -1 Add '2x' to each side of the equation. -1i2 + -2x + 2x + x2 = -1 + 2x Combine like terms: -2x + 2x = 0 -1i2 + 0 + x2 = -1 + 2x -1i2 + x2 = -1 + 2x Add '-1x2' to each side of the equation. -1i2 + x2 + -1x2 = -1 + 2x + -1x2 Combine like terms: x2 + -1x2 = 0 -1i2 + 0 = -1 + 2x + -1x2 -1i2 = -1 + 2x + -1x2 Divide each side by '-1'. i2 = 1 + -2x + x2 Simplifying i2 = 1 + -2x + x2 Reorder the terms: -1 + i2 + 2x + -1x2 = 1 + -2x + x2 + -1 + 2x + -1x2 Reorder the terms: -1 + i2 + 2x + -1x2 = 1 + -1 + -2x + 2x + x2 + -1x2 Combine like terms: 1 + -1 = 0 -1 + i2 + 2x + -1x2 = 0 + -2x + 2x + x2 + -1x2 -1 + i2 + 2x + -1x2 = -2x + 2x + x2 + -1x2 Combine like terms: -2x + 2x = 0 -1 + i2 + 2x + -1x2 = 0 + x2 + -1x2 -1 + i2 + 2x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -1 + i2 + 2x + -1x2 = 0 The solution to this equation could not be determined.
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