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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. (5 + -4i)(3 + 7i) = 0Subproblem 1
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 = 1.25Subproblem 2
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 = -0.4285714286Solution
i = {1.25, -0.4285714286}
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