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Simplifying y = [x + (1 + 2i)][x + (1 + -2i)] Remove parenthesis around (1 + 2i) y = [x + 1 + 2i][x + (1 + -2i)] Reorder the terms: y = [1 + 2i + x][x + (1 + -2i)] Remove parenthesis around (1 + -2i) y = [1 + 2i + x][x + 1 + -2i] Reorder the terms: y = [1 + 2i + x][1 + -2i + x] Multiply [1 + 2i + x] * [1 + -2i + x] y = [1[1 + -2i + x] + 2i * [1 + -2i + x] + x[1 + -2i + x]] y = [[1 * 1 + -2i * 1 + x * 1] + 2i * [1 + -2i + x] + x[1 + -2i + x]] y = [[1 + -2i + 1x] + 2i * [1 + -2i + x] + x[1 + -2i + x]] y = [1 + -2i + 1x + [1 * 2i + -2i * 2i + x * 2i] + x[1 + -2i + x]] Reorder the terms: y = [1 + -2i + 1x + [2i + 2ix + -4i2] + x[1 + -2i + x]] y = [1 + -2i + 1x + [2i + 2ix + -4i2] + x[1 + -2i + x]] y = [1 + -2i + 1x + 2i + 2ix + -4i2 + [1 * x + -2i * x + x * x]] Reorder the terms: y = [1 + -2i + 1x + 2i + 2ix + -4i2 + [-2ix + 1x + x2]] y = [1 + -2i + 1x + 2i + 2ix + -4i2 + [-2ix + 1x + x2]] Reorder the terms: y = [1 + -2i + 2i + 2ix + -2ix + -4i2 + 1x + 1x + x2] Combine like terms: -2i + 2i = 0 y = [1 + 0 + 2ix + -2ix + -4i2 + 1x + 1x + x2] y = [1 + 2ix + -2ix + -4i2 + 1x + 1x + x2] Combine like terms: 2ix + -2ix = 0 y = [1 + 0 + -4i2 + 1x + 1x + x2] y = [1 + -4i2 + 1x + 1x + x2] Combine like terms: 1x + 1x = 2x y = [1 + -4i2 + 2x + x2] Solving y = 1 + -4i2 + 2x + x2 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Simplifying y = 1 + -4i2 + 2x + x2
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