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Simplifying (3i + 1)(2i + -1) = 0 Reorder the terms: (1 + 3i)(2i + -1) = 0 Reorder the terms: (1 + 3i)(-1 + 2i) = 0 Multiply (1 + 3i) * (-1 + 2i) (1(-1 + 2i) + 3i * (-1 + 2i)) = 0 ((-1 * 1 + 2i * 1) + 3i * (-1 + 2i)) = 0 ((-1 + 2i) + 3i * (-1 + 2i)) = 0 (-1 + 2i + (-1 * 3i + 2i * 3i)) = 0 (-1 + 2i + (-3i + 6i2)) = 0 Combine like terms: 2i + -3i = -1i (-1 + -1i + 6i2) = 0 Solving -1 + -1i + 6i2 = 0 Solving for variable 'i'. Factor a trinomial. (-1 + -3i)(1 + -2i) = 0Subproblem 1
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 = -0.3333333333Subproblem 2
Set the factor '(1 + -2i)' equal to zero and attempt to solve: Simplifying 1 + -2i = 0 Solving 1 + -2i = 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 + -2i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2i = 0 + -1 -2i = 0 + -1 Combine like terms: 0 + -1 = -1 -2i = -1 Divide each side by '-2'. i = 0.5 Simplifying i = 0.5Solution
i = {-0.3333333333, 0.5}
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