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Simplifying (6 + -7i)(5 + i) = 0 Multiply (6 + -7i) * (5 + i) (6(5 + i) + -7i * (5 + i)) = 0 ((5 * 6 + i * 6) + -7i * (5 + i)) = 0 ((30 + 6i) + -7i * (5 + i)) = 0 (30 + 6i + (5 * -7i + i * -7i)) = 0 (30 + 6i + (-35i + -7i2)) = 0 Combine like terms: 6i + -35i = -29i (30 + -29i + -7i2) = 0 Solving 30 + -29i + -7i2 = 0 Solving for variable 'i'. Factor a trinomial. (6 + -7i)(5 + i) = 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 + i)' equal to zero and attempt to solve: Simplifying 5 + i = 0 Solving 5 + i = 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 + i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + i = 0 + -5 i = 0 + -5 Combine like terms: 0 + -5 = -5 i = -5 Simplifying i = -5Solution
i = {0.8571428571, -5}
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