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Simplifying (1 + -3i)(3 + 4i) = 0 Multiply (1 + -3i) * (3 + 4i) (1(3 + 4i) + -3i * (3 + 4i)) = 0 ((3 * 1 + 4i * 1) + -3i * (3 + 4i)) = 0 ((3 + 4i) + -3i * (3 + 4i)) = 0 (3 + 4i + (3 * -3i + 4i * -3i)) = 0 (3 + 4i + (-9i + -12i2)) = 0 Combine like terms: 4i + -9i = -5i (3 + -5i + -12i2) = 0 Solving 3 + -5i + -12i2 = 0 Solving for variable 'i'. Factor a trinomial. (1 + -3i)(3 + 4i) = 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 '(3 + 4i)' equal to zero and attempt to solve: Simplifying 3 + 4i = 0 Solving 3 + 4i = 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 + 4i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4i = 0 + -3 4i = 0 + -3 Combine like terms: 0 + -3 = -3 4i = -3 Divide each side by '4'. i = -0.75 Simplifying i = -0.75Solution
i = {0.3333333333, -0.75}
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