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Simplifying (x + (1 + i))(x + -1(x + i)) = 0 Remove parenthesis around (1 + i) (x + 1 + i)(x + -1(x + i)) = 0 Reorder the terms: (1 + i + x)(x + -1(x + i)) = 0 Reorder the terms: (1 + i + x)(x + -1(i + x)) = 0 (1 + i + x)(x + (i * -1 + x * -1)) = 0 (1 + i + x)(x + (-1i + -1x)) = 0 Reorder the terms: (1 + i + x)(-1i + x + -1x) = 0 Combine like terms: x + -1x = 0 (1 + i + x)(-1i + 0) = 0 (1 + i + x)(-1i) = 0 Remove parenthesis around (-1i) (1 + i + x) * -1i = 0 Reorder the terms for easier multiplication: -1i(1 + i + x) = 0 (1 * -1i + i * -1i + x * -1i) = 0 Reorder the terms: (-1i + -1ix + -1i2) = 0 (-1i + -1ix + -1i2) = 0 Solving -1i + -1ix + -1i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '-1i'. -1i(1 + x + i) = 0 Ignore the factor -1.Subproblem 1
Set the factor 'i' equal to zero and attempt to solve: Simplifying i = 0 Solving i = 0 Move all terms containing i to the left, all other terms to the right. Simplifying i = 0Subproblem 2
Set the factor '(1 + x + i)' equal to zero and attempt to solve: Simplifying 1 + x + i = 0 Reorder the terms: 1 + i + x = 0 Solving 1 + i + x = 0 Move all terms containing i to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + i + -1 + x = 0 + -1 Reorder the terms: 1 + -1 + i + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + i + x = 0 + -1 i + x = 0 + -1 Combine like terms: 0 + -1 = -1 i + x = -1 Add '-1x' to each side of the equation. i + x + -1x = -1 + -1x Combine like terms: x + -1x = 0 i + 0 = -1 + -1x i = -1 + -1x Simplifying i = -1 + -1xSolution
i = {0, -1 + -1x}
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