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Simplifying (6 + 9i)(5 + -23i) = 0 Multiply (6 + 9i) * (5 + -23i) (6(5 + -23i) + 9i * (5 + -23i)) = 0 ((5 * 6 + -23i * 6) + 9i * (5 + -23i)) = 0 ((30 + -138i) + 9i * (5 + -23i)) = 0 (30 + -138i + (5 * 9i + -23i * 9i)) = 0 (30 + -138i + (45i + -207i2)) = 0 Combine like terms: -138i + 45i = -93i (30 + -93i + -207i2) = 0 Solving 30 + -93i + -207i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '3'. 3(10 + -31i + -69i2) = 0 Factor a trinomial. 3((5 + -23i)(2 + 3i)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(5 + -23i)' equal to zero and attempt to solve: Simplifying 5 + -23i = 0 Solving 5 + -23i = 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 + -23i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -23i = 0 + -5 -23i = 0 + -5 Combine like terms: 0 + -5 = -5 -23i = -5 Divide each side by '-23'. i = 0.2173913043 Simplifying i = 0.2173913043Subproblem 2
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 = -0.6666666667Solution
i = {0.2173913043, -0.6666666667}
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