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Simplifying (4 + -6i)(7 + -8i) = 0 Multiply (4 + -6i) * (7 + -8i) (4(7 + -8i) + -6i * (7 + -8i)) = 0 ((7 * 4 + -8i * 4) + -6i * (7 + -8i)) = 0 ((28 + -32i) + -6i * (7 + -8i)) = 0 (28 + -32i + (7 * -6i + -8i * -6i)) = 0 (28 + -32i + (-42i + 48i2)) = 0 Combine like terms: -32i + -42i = -74i (28 + -74i + 48i2) = 0 Solving 28 + -74i + 48i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '2'. 2(14 + -37i + 24i2) = 0 Factor a trinomial. 2((2 + -3i)(7 + -8i)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(2 + -3i)' equal to zero and attempt to solve: Simplifying 2 + -3i = 0 Solving 2 + -3i = 0 Move all terms containing i to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3i = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3i = 0 + -2 -3i = 0 + -2 Combine like terms: 0 + -2 = -2 -3i = -2 Divide each side by '-3'. i = 0.6666666667 Simplifying i = 0.6666666667Subproblem 2
Set the factor '(7 + -8i)' equal to zero and attempt to solve: Simplifying 7 + -8i = 0 Solving 7 + -8i = 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 + -8i = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -8i = 0 + -7 -8i = 0 + -7 Combine like terms: 0 + -7 = -7 -8i = -7 Divide each side by '-8'. i = 0.875 Simplifying i = 0.875Solution
i = {0.6666666667, 0.875}
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