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Simplifying (-1 + 3i)(2 + -1i) = 0 Multiply (-1 + 3i) * (2 + -1i) (-1(2 + -1i) + 3i * (2 + -1i)) = 0 ((2 * -1 + -1i * -1) + 3i * (2 + -1i)) = 0 ((-2 + 1i) + 3i * (2 + -1i)) = 0 (-2 + 1i + (2 * 3i + -1i * 3i)) = 0 (-2 + 1i + (6i + -3i2)) = 0 Combine like terms: 1i + 6i = 7i (-2 + 7i + -3i2) = 0 Solving -2 + 7i + -3i2 = 0 Solving for variable 'i'. Factor a trinomial. (-2 + i)(1 + -3i) = 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 + -3i)' equal to zero and attempt to solve: Simplifying 1 + -3i = 0 Solving 1 + -3i = 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 + -3i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3i = 0 + -1 -3i = 0 + -1 Combine like terms: 0 + -1 = -1 -3i = -1 Divide each side by '-3'. i = 0.3333333333 Simplifying i = 0.3333333333Solution
i = {2, 0.3333333333}
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