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Simplifying f(x) = (x + -3i)(x + -1(2 + -1i)) Multiply f * x fx = (x + -3i)(x + -1(2 + -1i)) Reorder the terms: fx = (-3i + x)(x + -1(2 + -1i)) fx = (-3i + x)(x + (2 * -1 + -1i * -1)) fx = (-3i + x)(x + (-2 + 1i)) Reorder the terms: fx = (-3i + x)(-2 + 1i + x) Multiply (-3i + x) * (-2 + 1i + x) fx = (-3i * (-2 + 1i + x) + x(-2 + 1i + x)) fx = ((-2 * -3i + 1i * -3i + x * -3i) + x(-2 + 1i + x)) Reorder the terms: fx = ((6i + -3ix + -3i2) + x(-2 + 1i + x)) fx = ((6i + -3ix + -3i2) + x(-2 + 1i + x)) fx = (6i + -3ix + -3i2 + (-2 * x + 1i * x + x * x)) Reorder the terms: fx = (6i + -3ix + -3i2 + (1ix + -2x + x2)) fx = (6i + -3ix + -3i2 + (1ix + -2x + x2)) Reorder the terms: fx = (6i + -3ix + 1ix + -3i2 + -2x + x2) Combine like terms: -3ix + 1ix = -2ix fx = (6i + -2ix + -3i2 + -2x + x2) Solving fx = 6i + -2ix + -3i2 + -2x + 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 = 6ix-1 + -2i + -3i2x-1 + -2 + x Simplifying f = 6ix-1 + -2i + -3i2x-1 + -2 + x Reorder the terms: f = -2 + -2i + 6ix-1 + -3i2x-1 + x
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