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Simplifying (7 + -6i)(-8 + 3i) = 0 Multiply (7 + -6i) * (-8 + 3i) (7(-8 + 3i) + -6i * (-8 + 3i)) = 0 ((-8 * 7 + 3i * 7) + -6i * (-8 + 3i)) = 0 ((-56 + 21i) + -6i * (-8 + 3i)) = 0 (-56 + 21i + (-8 * -6i + 3i * -6i)) = 0 (-56 + 21i + (48i + -18i2)) = 0 Combine like terms: 21i + 48i = 69i (-56 + 69i + -18i2) = 0 Solving -56 + 69i + -18i2 = 0 Solving for variable 'i'. Factor a trinomial. (-8 + 3i)(7 + -6i) = 0Subproblem 1
Set the factor '(-8 + 3i)' equal to zero and attempt to solve: Simplifying -8 + 3i = 0 Solving -8 + 3i = 0 Move all terms containing i to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + 3i = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 3i = 0 + 8 3i = 0 + 8 Combine like terms: 0 + 8 = 8 3i = 8 Divide each side by '3'. i = 2.666666667 Simplifying i = 2.666666667Subproblem 2
Set the factor '(7 + -6i)' equal to zero and attempt to solve: Simplifying 7 + -6i = 0 Solving 7 + -6i = 0 Move all terms containing i to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -6i = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -6i = 0 + -7 -6i = 0 + -7 Combine like terms: 0 + -7 = -7 -6i = -7 Divide each side by '-6'. i = 1.166666667 Simplifying i = 1.166666667Solution
i = {2.666666667, 1.166666667}
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