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Simplifying f(5i) = x3 + (7 + -5i) * x2 + (6 + -35i) * x + -30i Remove parenthesis around (5i) f * 5i = x3 + (7 + -5i) * x2 + (6 + -35i) * x + -30i Reorder the terms for easier multiplication: 5f * i = x3 + (7 + -5i) * x2 + (6 + -35i) * x + -30i Multiply f * i 5fi = x3 + (7 + -5i) * x2 + (6 + -35i) * x + -30i Reorder the terms for easier multiplication: 5fi = x3 + x2(7 + -5i) + (6 + -35i) * x + -30i 5fi = x3 + (7 * x2 + -5i * x2) + (6 + -35i) * x + -30i Reorder the terms: 5fi = x3 + (-5ix2 + 7x2) + (6 + -35i) * x + -30i 5fi = x3 + (-5ix2 + 7x2) + (6 + -35i) * x + -30i Reorder the terms for easier multiplication: 5fi = x3 + -5ix2 + 7x2 + x(6 + -35i) + -30i 5fi = x3 + -5ix2 + 7x2 + (6 * x + -35i * x) + -30i Reorder the terms: 5fi = x3 + -5ix2 + 7x2 + (-35ix + 6x) + -30i 5fi = x3 + -5ix2 + 7x2 + (-35ix + 6x) + -30i Reorder the terms: 5fi = -30i + -35ix + -5ix2 + 6x + 7x2 + x3 Solving 5fi = -30i + -35ix + -5ix2 + 6x + 7x2 + x3 Solving for variable 'f'. Move all terms containing f to the left, all other terms to the right. Divide each side by '5i'. f = -6 + -7x + -1x2 + 1.2i-1x + 1.4i-1x2 + 0.2i-1x3 Simplifying f = -6 + -7x + -1x2 + 1.2i-1x + 1.4i-1x2 + 0.2i-1x3 Reorder the terms: f = -6 + 1.2i-1x + 1.4i-1x2 + 0.2i-1x3 + -7x + -1x2
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