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Simplifying (5 + 3i)(3 + -4i) = 0 Multiply (5 + 3i) * (3 + -4i) (5(3 + -4i) + 3i * (3 + -4i)) = 0 ((3 * 5 + -4i * 5) + 3i * (3 + -4i)) = 0 ((15 + -20i) + 3i * (3 + -4i)) = 0 (15 + -20i + (3 * 3i + -4i * 3i)) = 0 (15 + -20i + (9i + -12i2)) = 0 Combine like terms: -20i + 9i = -11i (15 + -11i + -12i2) = 0 Solving 15 + -11i + -12i2 = 0 Solving for variable 'i'. Factor a trinomial. (3 + -4i)(5 + 3i) = 0Subproblem 1
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 = 0.75Subproblem 2
Set the factor '(5 + 3i)' equal to zero and attempt to solve: Simplifying 5 + 3i = 0 Solving 5 + 3i = 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 + 3i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 3i = 0 + -5 3i = 0 + -5 Combine like terms: 0 + -5 = -5 3i = -5 Divide each side by '3'. i = -1.666666667 Simplifying i = -1.666666667Solution
i = {0.75, -1.666666667}
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