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Simplifying x3 + 2x2 + x(1 + -1i) + 1 = 0 x3 + 2x2 + (1 * x + -1i * x) + 1 = 0 Reorder the terms: x3 + 2x2 + (-1ix + 1x) + 1 = 0 x3 + 2x2 + (-1ix + 1x) + 1 = 0 Reorder the terms: 1 + -1ix + 1x + 2x2 + x3 = 0 Solving 1 + -1ix + 1x + 2x2 + x3 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1ix + 1x + 2x2 + -1 + x3 = 0 + -1 Reorder the terms: 1 + -1 + -1ix + 1x + 2x2 + x3 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1ix + 1x + 2x2 + x3 = 0 + -1 -1ix + 1x + 2x2 + x3 = 0 + -1 Combine like terms: 0 + -1 = -1 -1ix + 1x + 2x2 + x3 = -1 Add '-1x' to each side of the equation. -1ix + 1x + 2x2 + -1x + x3 = -1 + -1x Reorder the terms: -1ix + 1x + -1x + 2x2 + x3 = -1 + -1x Combine like terms: 1x + -1x = 0 -1ix + 0 + 2x2 + x3 = -1 + -1x -1ix + 2x2 + x3 = -1 + -1x Add '-2x2' to each side of the equation. -1ix + 2x2 + -2x2 + x3 = -1 + -1x + -2x2 Combine like terms: 2x2 + -2x2 = 0 -1ix + 0 + x3 = -1 + -1x + -2x2 -1ix + x3 = -1 + -1x + -2x2 Add '-1x3' to each side of the equation. -1ix + x3 + -1x3 = -1 + -1x + -2x2 + -1x3 Combine like terms: x3 + -1x3 = 0 -1ix + 0 = -1 + -1x + -2x2 + -1x3 -1ix = -1 + -1x + -2x2 + -1x3 Divide each side by '-1x'. i = x-1 + 1 + 2x + x2 Simplifying i = x-1 + 1 + 2x + x2 Reorder the terms: i = 1 + x-1 + 2x + x2
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