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Simplifying x2 + (1 + -1i) * x + -1 = 0 Reorder the terms for easier multiplication: x2 + x(1 + -1i) + -1 = 0 x2 + (1 * x + -1i * x) + -1 = 0 Reorder the terms: x2 + (-1ix + 1x) + -1 = 0 x2 + (-1ix + 1x) + -1 = 0 Reorder the terms: -1 + -1ix + 1x + x2 = 0 Solving -1 + -1ix + 1x + x2 = 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 + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -1ix + 1x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1ix + 1x + x2 = 0 + 1 -1ix + 1x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -1ix + 1x + x2 = 1 Add '-1x' to each side of the equation. -1ix + 1x + -1x + x2 = 1 + -1x Combine like terms: 1x + -1x = 0 -1ix + 0 + x2 = 1 + -1x -1ix + x2 = 1 + -1x Add '-1x2' to each side of the equation. -1ix + x2 + -1x2 = 1 + -1x + -1x2 Combine like terms: x2 + -1x2 = 0 -1ix + 0 = 1 + -1x + -1x2 -1ix = 1 + -1x + -1x2 Divide each side by '-1x'. i = -1x-1 + 1 + x Simplifying i = -1x-1 + 1 + x Reorder the terms: i = 1 + -1x-1 + x
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