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Simplifying (6 + -7i)(8 + -3i) = 0 Multiply (6 + -7i) * (8 + -3i) (6(8 + -3i) + -7i * (8 + -3i)) = 0 ((8 * 6 + -3i * 6) + -7i * (8 + -3i)) = 0 ((48 + -18i) + -7i * (8 + -3i)) = 0 (48 + -18i + (8 * -7i + -3i * -7i)) = 0 (48 + -18i + (-56i + 21i2)) = 0 Combine like terms: -18i + -56i = -74i (48 + -74i + 21i2) = 0 Solving 48 + -74i + 21i2 = 0 Solving for variable 'i'. Factor a trinomial. (6 + -7i)(8 + -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 '(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 = 2.666666667Solution
i = {0.8571428571, 2.666666667}
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