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Simplifying (1 + 2i)(3 + i) = 0 Multiply (1 + 2i) * (3 + i) (1(3 + i) + 2i * (3 + i)) = 0 ((3 * 1 + i * 1) + 2i * (3 + i)) = 0 ((3 + 1i) + 2i * (3 + i)) = 0 (3 + 1i + (3 * 2i + i * 2i)) = 0 (3 + 1i + (6i + 2i2)) = 0 Combine like terms: 1i + 6i = 7i (3 + 7i + 2i2) = 0 Solving 3 + 7i + 2i2 = 0 Solving for variable 'i'. Factor a trinomial. (3 + i)(1 + 2i) = 0Subproblem 1
Set the factor '(3 + i)' equal to zero and attempt to solve: Simplifying 3 + i = 0 Solving 3 + i = 0 Move all terms containing i to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + i = 0 + -3 i = 0 + -3 Combine like terms: 0 + -3 = -3 i = -3 Simplifying i = -3Subproblem 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 = {-3, -0.5}
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