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Simplifying (2 + -1i)(1 + 3i) = 0 Multiply (2 + -1i) * (1 + 3i) (2(1 + 3i) + -1i * (1 + 3i)) = 0 ((1 * 2 + 3i * 2) + -1i * (1 + 3i)) = 0 ((2 + 6i) + -1i * (1 + 3i)) = 0 (2 + 6i + (1 * -1i + 3i * -1i)) = 0 (2 + 6i + (-1i + -3i2)) = 0 Combine like terms: 6i + -1i = 5i (2 + 5i + -3i2) = 0 Solving 2 + 5i + -3i2 = 0 Solving for variable 'i'. Factor a trinomial. (2 + -1i)(1 + 3i) = 0Subproblem 1
Set the factor '(2 + -1i)' equal to zero and attempt to solve: Simplifying 2 + -1i = 0 Solving 2 + -1i = 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 + -1i = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1i = 0 + -2 -1i = 0 + -2 Combine like terms: 0 + -2 = -2 -1i = -2 Divide each side by '-1'. 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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