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Simplifying y = (x + -1 + 3i)(x + -1 + -3i) Reorder the terms: y = (-1 + 3i + x)(x + -1 + -3i) Reorder the terms: y = (-1 + 3i + x)(-1 + -3i + x) Multiply (-1 + 3i + x) * (-1 + -3i + x) y = (-1(-1 + -3i + x) + 3i * (-1 + -3i + x) + x(-1 + -3i + x)) y = ((-1 * -1 + -3i * -1 + x * -1) + 3i * (-1 + -3i + x) + x(-1 + -3i + x)) y = ((1 + 3i + -1x) + 3i * (-1 + -3i + x) + x(-1 + -3i + x)) y = (1 + 3i + -1x + (-1 * 3i + -3i * 3i + x * 3i) + x(-1 + -3i + x)) Reorder the terms: y = (1 + 3i + -1x + (-3i + 3ix + -9i2) + x(-1 + -3i + x)) y = (1 + 3i + -1x + (-3i + 3ix + -9i2) + x(-1 + -3i + x)) y = (1 + 3i + -1x + -3i + 3ix + -9i2 + (-1 * x + -3i * x + x * x)) Reorder the terms: y = (1 + 3i + -1x + -3i + 3ix + -9i2 + (-3ix + -1x + x2)) y = (1 + 3i + -1x + -3i + 3ix + -9i2 + (-3ix + -1x + x2)) Reorder the terms: y = (1 + 3i + -3i + 3ix + -3ix + -9i2 + -1x + -1x + x2) Combine like terms: 3i + -3i = 0 y = (1 + 0 + 3ix + -3ix + -9i2 + -1x + -1x + x2) y = (1 + 3ix + -3ix + -9i2 + -1x + -1x + x2) Combine like terms: 3ix + -3ix = 0 y = (1 + 0 + -9i2 + -1x + -1x + x2) y = (1 + -9i2 + -1x + -1x + x2) Combine like terms: -1x + -1x = -2x y = (1 + -9i2 + -2x + x2) Solving y = 1 + -9i2 + -2x + x2 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Simplifying y = 1 + -9i2 + -2x + x2
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