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Simplifying 2i(1 + -1I)(1 + -1i) = 0 Multiply (1 + -1I) * (1 + -1i) 2i(1(1 + -1i) + -1I * (1 + -1i)) = 0 2i((1 * 1 + -1i * 1) + -1I * (1 + -1i)) = 0 2i((1 + -1i) + -1I * (1 + -1i)) = 0 2i(1 + -1i + (1 * -1I + -1i * -1I)) = 0 2i(1 + -1i + (-1I + 1iI)) = 0 Reorder the terms: 2i(1 + -1I + -1i + 1iI) = 0 2i(1 + -1I + -1i + 1iI) = 0 (1 * 2i + -1I * 2i + -1i * 2i + 1iI * 2i) = 0 (2i + -2iI + -2i2 + 2i2I) = 0 Solving 2i + -2iI + -2i2 + 2i2I = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '2i'. 2i(1 + -1I + -1i + iI) = 0 Ignore the factor 2.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 + -1I + -1i + iI)' equal to zero and attempt to solve: Simplifying 1 + -1I + -1i + iI = 0 Solving 1 + -1I + -1i + iI = 0 Move all terms containing i to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1I + -1i + -1 + iI = 0 + -1 Reorder the terms: 1 + -1 + -1I + -1i + iI = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1I + -1i + iI = 0 + -1 -1I + -1i + iI = 0 + -1 Combine like terms: 0 + -1 = -1 -1I + -1i + iI = -1 Add 'I' to each side of the equation. -1I + -1i + I + iI = -1 + I Reorder the terms: -1I + I + -1i + iI = -1 + I Combine like terms: -1I + I = 0 0 + -1i + iI = -1 + I -1i + iI = -1 + I The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
i = {0}
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