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Simplifying f(X) = (x + -1(3 + 2i))(x + -1(3 + -2i)) Multiply f * X fX = (x + -1(3 + 2i))(x + -1(3 + -2i)) fX = (x + (3 * -1 + 2i * -1))(x + -1(3 + -2i)) fX = (x + (-3 + -2i))(x + -1(3 + -2i)) Reorder the terms: fX = (-3 + -2i + x)(x + -1(3 + -2i)) fX = (-3 + -2i + x)(x + (3 * -1 + -2i * -1)) fX = (-3 + -2i + x)(x + (-3 + 2i)) Reorder the terms: fX = (-3 + -2i + x)(-3 + 2i + x) Multiply (-3 + -2i + x) * (-3 + 2i + x) fX = (-3(-3 + 2i + x) + -2i * (-3 + 2i + x) + x(-3 + 2i + x)) fX = ((-3 * -3 + 2i * -3 + x * -3) + -2i * (-3 + 2i + x) + x(-3 + 2i + x)) fX = ((9 + -6i + -3x) + -2i * (-3 + 2i + x) + x(-3 + 2i + x)) fX = (9 + -6i + -3x + (-3 * -2i + 2i * -2i + x * -2i) + x(-3 + 2i + x)) Reorder the terms: fX = (9 + -6i + -3x + (6i + -2ix + -4i2) + x(-3 + 2i + x)) fX = (9 + -6i + -3x + (6i + -2ix + -4i2) + x(-3 + 2i + x)) fX = (9 + -6i + -3x + 6i + -2ix + -4i2 + (-3 * x + 2i * x + x * x)) Reorder the terms: fX = (9 + -6i + -3x + 6i + -2ix + -4i2 + (2ix + -3x + x2)) fX = (9 + -6i + -3x + 6i + -2ix + -4i2 + (2ix + -3x + x2)) Reorder the terms: fX = (9 + -6i + 6i + -2ix + 2ix + -4i2 + -3x + -3x + x2) Combine like terms: -6i + 6i = 0 fX = (9 + 0 + -2ix + 2ix + -4i2 + -3x + -3x + x2) fX = (9 + -2ix + 2ix + -4i2 + -3x + -3x + x2) Combine like terms: -2ix + 2ix = 0 fX = (9 + 0 + -4i2 + -3x + -3x + x2) fX = (9 + -4i2 + -3x + -3x + x2) Combine like terms: -3x + -3x = -6x fX = (9 + -4i2 + -6x + x2) Solving fX = 9 + -4i2 + -6x + x2 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Divide each side by 'X'. f = 9X-1 + -4i2X-1 + -6xX-1 + x2X-1 Simplifying f = 9X-1 + -4i2X-1 + -6xX-1 + x2X-1
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