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Simplifying (1 + -1i)(i + -2) = 0 Reorder the terms: (1 + -1i)(-2 + i) = 0 Multiply (1 + -1i) * (-2 + i) (1(-2 + i) + -1i * (-2 + i)) = 0 ((-2 * 1 + i * 1) + -1i * (-2 + i)) = 0 ((-2 + 1i) + -1i * (-2 + i)) = 0 (-2 + 1i + (-2 * -1i + i * -1i)) = 0 (-2 + 1i + (2i + -1i2)) = 0 Combine like terms: 1i + 2i = 3i (-2 + 3i + -1i2) = 0 Solving -2 + 3i + -1i2 = 0 Solving for variable 'i'. Factor a trinomial. (-2 + i)(1 + -1i) = 0Subproblem 1
Set the factor '(-2 + i)' equal to zero and attempt to solve: Simplifying -2 + i = 0 Solving -2 + i = 0 Move all terms containing i to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + i = 0 + 2 Combine like terms: -2 + 2 = 0 0 + i = 0 + 2 i = 0 + 2 Combine like terms: 0 + 2 = 2 i = 2 Simplifying i = 2Subproblem 2
Set the factor '(1 + -1i)' equal to zero and attempt to solve: Simplifying 1 + -1i = 0 Solving 1 + -1i = 0 Move all terms containing i to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1i = 0 + -1 -1i = 0 + -1 Combine like terms: 0 + -1 = -1 -1i = -1 Divide each side by '-1'. i = 1 Simplifying i = 1Solution
i = {2, 1}
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