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Simplifying (3 + -7i)(8 + -6i) = 0 Multiply (3 + -7i) * (8 + -6i) (3(8 + -6i) + -7i * (8 + -6i)) = 0 ((8 * 3 + -6i * 3) + -7i * (8 + -6i)) = 0 ((24 + -18i) + -7i * (8 + -6i)) = 0 (24 + -18i + (8 * -7i + -6i * -7i)) = 0 (24 + -18i + (-56i + 42i2)) = 0 Combine like terms: -18i + -56i = -74i (24 + -74i + 42i2) = 0 Solving 24 + -74i + 42i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '2'. 2(12 + -37i + 21i2) = 0 Factor a trinomial. 2((3 + -7i)(4 + -3i)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + -7i)' equal to zero and attempt to solve: Simplifying 3 + -7i = 0 Solving 3 + -7i = 0 Move all terms containing i to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -7i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -7i = 0 + -3 -7i = 0 + -3 Combine like terms: 0 + -3 = -3 -7i = -3 Divide each side by '-7'. i = 0.4285714286 Simplifying i = 0.4285714286Subproblem 2
Set the factor '(4 + -3i)' equal to zero and attempt to solve: Simplifying 4 + -3i = 0 Solving 4 + -3i = 0 Move all terms containing i to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -3i = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3i = 0 + -4 -3i = 0 + -4 Combine like terms: 0 + -4 = -4 -3i = -4 Divide each side by '-3'. i = 1.333333333 Simplifying i = 1.333333333Solution
i = {0.4285714286, 1.333333333}
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