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Simplifying (5 + -9i)(6 + 7i) = 0 Multiply (5 + -9i) * (6 + 7i) (5(6 + 7i) + -9i * (6 + 7i)) = 0 ((6 * 5 + 7i * 5) + -9i * (6 + 7i)) = 0 ((30 + 35i) + -9i * (6 + 7i)) = 0 (30 + 35i + (6 * -9i + 7i * -9i)) = 0 (30 + 35i + (-54i + -63i2)) = 0 Combine like terms: 35i + -54i = -19i (30 + -19i + -63i2) = 0 Solving 30 + -19i + -63i2 = 0 Solving for variable 'i'. Factor a trinomial. (5 + -9i)(6 + 7i) = 0Subproblem 1
Set the factor '(5 + -9i)' equal to zero and attempt to solve: Simplifying 5 + -9i = 0 Solving 5 + -9i = 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 + -9i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -9i = 0 + -5 -9i = 0 + -5 Combine like terms: 0 + -5 = -5 -9i = -5 Divide each side by '-9'. i = 0.5555555556 Simplifying i = 0.5555555556Subproblem 2
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 = -0.8571428571Solution
i = {0.5555555556, -0.8571428571}
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