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Simplifying (7 + 4i)(3 + -5i) = 0 Multiply (7 + 4i) * (3 + -5i) (7(3 + -5i) + 4i * (3 + -5i)) = 0 ((3 * 7 + -5i * 7) + 4i * (3 + -5i)) = 0 ((21 + -35i) + 4i * (3 + -5i)) = 0 (21 + -35i + (3 * 4i + -5i * 4i)) = 0 (21 + -35i + (12i + -20i2)) = 0 Combine like terms: -35i + 12i = -23i (21 + -23i + -20i2) = 0 Solving 21 + -23i + -20i2 = 0 Solving for variable 'i'. Factor a trinomial. (3 + -5i)(7 + 4i) = 0Subproblem 1
Set the factor '(3 + -5i)' equal to zero and attempt to solve: Simplifying 3 + -5i = 0 Solving 3 + -5i = 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 + -5i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5i = 0 + -3 -5i = 0 + -3 Combine like terms: 0 + -3 = -3 -5i = -3 Divide each side by '-5'. i = 0.6 Simplifying i = 0.6Subproblem 2
Set the factor '(7 + 4i)' equal to zero and attempt to solve: Simplifying 7 + 4i = 0 Solving 7 + 4i = 0 Move all terms containing i to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 4i = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 4i = 0 + -7 4i = 0 + -7 Combine like terms: 0 + -7 = -7 4i = -7 Divide each side by '4'. i = -1.75 Simplifying i = -1.75Solution
i = {0.6, -1.75}
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