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Simplifying (5 + 3i)(6 + -7i) = 0 Multiply (5 + 3i) * (6 + -7i) (5(6 + -7i) + 3i * (6 + -7i)) = 0 ((6 * 5 + -7i * 5) + 3i * (6 + -7i)) = 0 ((30 + -35i) + 3i * (6 + -7i)) = 0 (30 + -35i + (6 * 3i + -7i * 3i)) = 0 (30 + -35i + (18i + -21i2)) = 0 Combine like terms: -35i + 18i = -17i (30 + -17i + -21i2) = 0 Solving 30 + -17i + -21i2 = 0 Solving for variable 'i'. Factor a trinomial. (6 + -7i)(5 + 3i) = 0Subproblem 1
Set the factor '(6 + -7i)' equal to zero and attempt to solve: Simplifying 6 + -7i = 0 Solving 6 + -7i = 0 Move all terms containing i to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -7i = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -7i = 0 + -6 -7i = 0 + -6 Combine like terms: 0 + -6 = -6 -7i = -6 Divide each side by '-7'. i = 0.8571428571 Simplifying i = 0.8571428571Subproblem 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 = {0.8571428571, -1.666666667}
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