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Simplifying (5 + 4i)(3 + -7i) = 0 Multiply (5 + 4i) * (3 + -7i) (5(3 + -7i) + 4i * (3 + -7i)) = 0 ((3 * 5 + -7i * 5) + 4i * (3 + -7i)) = 0 ((15 + -35i) + 4i * (3 + -7i)) = 0 (15 + -35i + (3 * 4i + -7i * 4i)) = 0 (15 + -35i + (12i + -28i2)) = 0 Combine like terms: -35i + 12i = -23i (15 + -23i + -28i2) = 0 Solving 15 + -23i + -28i2 = 0 Solving for variable 'i'. Factor a trinomial. (3 + -7i)(5 + 4i) = 0Subproblem 1
Set the factor '(3 + -7i)' equal to zero and attempt to solve: Simplifying 3 + -7i = 0 Solving 3 + -7i = 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 + -7i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -7i = 0 + -3 -7i = 0 + -3 Combine like terms: 0 + -3 = -3 -7i = -3 Divide each side by '-7'. i = 0.4285714286 Simplifying i = 0.4285714286Subproblem 2
Set the factor '(5 + 4i)' equal to zero and attempt to solve: Simplifying 5 + 4i = 0 Solving 5 + 4i = 0 Move all terms containing i to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 4i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 4i = 0 + -5 4i = 0 + -5 Combine like terms: 0 + -5 = -5 4i = -5 Divide each side by '4'. i = -1.25 Simplifying i = -1.25Solution
i = {0.4285714286, -1.25}
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