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Simplifying (6 + 7i)(5 + 9i) = 0 Multiply (6 + 7i) * (5 + 9i) (6(5 + 9i) + 7i * (5 + 9i)) = 0 ((5 * 6 + 9i * 6) + 7i * (5 + 9i)) = 0 ((30 + 54i) + 7i * (5 + 9i)) = 0 (30 + 54i + (5 * 7i + 9i * 7i)) = 0 (30 + 54i + (35i + 63i2)) = 0 Combine like terms: 54i + 35i = 89i (30 + 89i + 63i2) = 0 Solving 30 + 89i + 63i2 = 0 Solving for variable 'i'. Factor a trinomial. (6 + 7i)(5 + 9i) = 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 + 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 = -0.5555555556Solution
i = {-0.8571428571, -0.5555555556}
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