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Simplifying f(x) = a[x + -1(1 + 2i)][x + -1(1 + -2i)] Multiply f * x fx = a[x + -1(1 + 2i)][x + -1(1 + -2i)] fx = a[x + (1 * -1 + 2i * -1)][x + -1(1 + -2i)] fx = a[x + (-1 + -2i)][x + -1(1 + -2i)] Reorder the terms: fx = a[-1 + -2i + x][x + -1(1 + -2i)] fx = a[-1 + -2i + x][x + (1 * -1 + -2i * -1)] fx = a[-1 + -2i + x][x + (-1 + 2i)] Reorder the terms: fx = a[-1 + -2i + x][-1 + 2i + x] Multiply [-1 + -2i + x] * [-1 + 2i + x] fx = a[-1[-1 + 2i + x] + -2i * [-1 + 2i + x] + x[-1 + 2i + x]] fx = a[[-1 * -1 + 2i * -1 + x * -1] + -2i * [-1 + 2i + x] + x[-1 + 2i + x]] fx = a[[1 + -2i + -1x] + -2i * [-1 + 2i + x] + x[-1 + 2i + x]] fx = a[1 + -2i + -1x + [-1 * -2i + 2i * -2i + x * -2i] + x[-1 + 2i + x]] Reorder the terms: fx = a[1 + -2i + -1x + [2i + -2ix + -4i2] + x[-1 + 2i + x]] fx = a[1 + -2i + -1x + [2i + -2ix + -4i2] + x[-1 + 2i + x]] fx = a[1 + -2i + -1x + 2i + -2ix + -4i2 + [-1 * x + 2i * x + x * x]] Reorder the terms: fx = a[1 + -2i + -1x + 2i + -2ix + -4i2 + [2ix + -1x + x2]] fx = a[1 + -2i + -1x + 2i + -2ix + -4i2 + [2ix + -1x + x2]] Reorder the terms: fx = a[1 + -2i + 2i + -2ix + 2ix + -4i2 + -1x + -1x + x2] Combine like terms: -2i + 2i = 0 fx = a[1 + 0 + -2ix + 2ix + -4i2 + -1x + -1x + x2] fx = a[1 + -2ix + 2ix + -4i2 + -1x + -1x + x2] Combine like terms: -2ix + 2ix = 0 fx = a[1 + 0 + -4i2 + -1x + -1x + x2] fx = a[1 + -4i2 + -1x + -1x + x2] Combine like terms: -1x + -1x = -2x fx = a[1 + -4i2 + -2x + x2] fx = [1 * a + -4i2 * a + -2x * a + x2 * a] fx = [1a + -4ai2 + -2ax + ax2] Solving fx = 1a + -4ai2 + -2ax + ax2 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Divide each side by 'x'. f = ax-1 + -4ai2x-1 + -2a + ax Simplifying f = ax-1 + -4ai2x-1 + -2a + ax Reorder the terms: f = -2a + -4ai2x-1 + ax-1 + ax
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