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Simplifying (x + -1)(x(1 + i))(x(1 + -1i)) = 0 Reorder the terms: (-1 + x)(x(1 + i))(x(1 + -1i)) = 0 (-1 + x)((1 * x + i * x))(x(1 + -1i)) = 0 Reorder the terms: (-1 + x)((ix + 1x))(x(1 + -1i)) = 0 (-1 + x)((ix + 1x))(x(1 + -1i)) = 0 (-1 + x)(ix + 1x)((1 * x + -1i * x)) = 0 Reorder the terms: (-1 + x)(ix + 1x)((-1ix + 1x)) = 0 (-1 + x)(ix + 1x)((-1ix + 1x)) = 0 Multiply (-1 + x) * (ix + 1x) (-1(ix + 1x) + x(ix + 1x))(-1ix + 1x) = 0 ((ix * -1 + 1x * -1) + x(ix + 1x))(-1ix + 1x) = 0 ((-1ix + -1x) + x(ix + 1x))(-1ix + 1x) = 0 (-1ix + -1x + (ix * x + 1x * x))(-1ix + 1x) = 0 (-1ix + -1x + (ix2 + 1x2))(-1ix + 1x) = 0 Reorder the terms: (-1ix + ix2 + -1x + 1x2)(-1ix + 1x) = 0 (-1ix + ix2 + -1x + 1x2)(-1ix + 1x) = 0 Multiply (-1ix + ix2 + -1x + 1x2) * (-1ix + 1x) (-1ix * (-1ix + 1x) + ix2(-1ix + 1x) + -1x * (-1ix + 1x) + 1x2 * (-1ix + 1x)) = 0 ((-1ix * -1ix + 1x * -1ix) + ix2(-1ix + 1x) + -1x * (-1ix + 1x) + 1x2 * (-1ix + 1x)) = 0 Reorder the terms: ((-1ix2 + 1i2x2) + ix2(-1ix + 1x) + -1x * (-1ix + 1x) + 1x2 * (-1ix + 1x)) = 0 ((-1ix2 + 1i2x2) + ix2(-1ix + 1x) + -1x * (-1ix + 1x) + 1x2 * (-1ix + 1x)) = 0 (-1ix2 + 1i2x2 + (-1ix * ix2 + 1x * ix2) + -1x * (-1ix + 1x) + 1x2 * (-1ix + 1x)) = 0 Reorder the terms: (-1ix2 + 1i2x2 + (1ix3 + -1i2x3) + -1x * (-1ix + 1x) + 1x2 * (-1ix + 1x)) = 0 (-1ix2 + 1i2x2 + (1ix3 + -1i2x3) + -1x * (-1ix + 1x) + 1x2 * (-1ix + 1x)) = 0 (-1ix2 + 1i2x2 + 1ix3 + -1i2x3 + (-1ix * -1x + 1x * -1x) + 1x2 * (-1ix + 1x)) = 0 (-1ix2 + 1i2x2 + 1ix3 + -1i2x3 + (1ix2 + -1x2) + 1x2 * (-1ix + 1x)) = 0 (-1ix2 + 1i2x2 + 1ix3 + -1i2x3 + 1ix2 + -1x2 + (-1ix * 1x2 + 1x * 1x2)) = 0 (-1ix2 + 1i2x2 + 1ix3 + -1i2x3 + 1ix2 + -1x2 + (-1ix3 + 1x3)) = 0 Reorder the terms: (-1ix2 + 1ix2 + 1ix3 + -1ix3 + 1i2x2 + -1i2x3 + -1x2 + 1x3) = 0 Combine like terms: -1ix2 + 1ix2 = 0 (0 + 1ix3 + -1ix3 + 1i2x2 + -1i2x3 + -1x2 + 1x3) = 0 (1ix3 + -1ix3 + 1i2x2 + -1i2x3 + -1x2 + 1x3) = 0 Combine like terms: 1ix3 + -1ix3 = 0 (0 + 1i2x2 + -1i2x3 + -1x2 + 1x3) = 0 (1i2x2 + -1i2x3 + -1x2 + 1x3) = 0 Solving 1i2x2 + -1i2x3 + -1x2 + 1x3 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add 'x2' to each side of the equation. 1i2x2 + -1i2x3 + -1x2 + x2 + 1x3 = 0 + x2 Combine like terms: -1x2 + x2 = 0 1i2x2 + -1i2x3 + 0 + 1x3 = 0 + x2 1i2x2 + -1i2x3 + 1x3 = 0 + x2 Remove the zero: 1i2x2 + -1i2x3 + 1x3 = x2 Add '-1x3' to each side of the equation. 1i2x2 + -1i2x3 + 1x3 + -1x3 = x2 + -1x3 Combine like terms: 1x3 + -1x3 = 0 1i2x2 + -1i2x3 + 0 = x2 + -1x3 1i2x2 + -1i2x3 = x2 + -1x3 Reorder the terms: 1i2x2 + -1i2x3 + -1x2 + x3 = x2 + -1x2 + -1x3 + x3 Combine like terms: x2 + -1x2 = 0 1i2x2 + -1i2x3 + -1x2 + x3 = 0 + -1x3 + x3 1i2x2 + -1i2x3 + -1x2 + x3 = -1x3 + x3 Combine like terms: -1x3 + x3 = 0 1i2x2 + -1i2x3 + -1x2 + x3 = 0 Factor out the Greatest Common Factor (GCF), 'x2'. x2(i2 + -1i2x + -1 + x) = 0Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing i to the left, all other terms to the right. Add '-1x2' to each side of the equation. x2 + -1x2 = 0 + -1x2 Remove the zero: 0 = -1x2 Simplifying 0 = -1x2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(i2 + -1i2x + -1 + x)' equal to zero and attempt to solve: Simplifying i2 + -1i2x + -1 + x = 0 Reorder the terms: -1 + i2 + -1i2x + x = 0 Solving -1 + i2 + -1i2x + 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 + i2 + -1i2x + 1 + x = 0 + 1 Reorder the terms: -1 + 1 + i2 + -1i2x + x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + i2 + -1i2x + x = 0 + 1 i2 + -1i2x + x = 0 + 1 Combine like terms: 0 + 1 = 1 i2 + -1i2x + x = 1 Add '-1x' to each side of the equation. i2 + -1i2x + x + -1x = 1 + -1x Combine like terms: x + -1x = 0 i2 + -1i2x + 0 = 1 + -1x i2 + -1i2x = 1 + -1x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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