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Simplifying (6 + 9i)(2 + -5i) = 0 Multiply (6 + 9i) * (2 + -5i) (6(2 + -5i) + 9i * (2 + -5i)) = 0 ((2 * 6 + -5i * 6) + 9i * (2 + -5i)) = 0 ((12 + -30i) + 9i * (2 + -5i)) = 0 (12 + -30i + (2 * 9i + -5i * 9i)) = 0 (12 + -30i + (18i + -45i2)) = 0 Combine like terms: -30i + 18i = -12i (12 + -12i + -45i2) = 0 Solving 12 + -12i + -45i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '3'. 3(4 + -4i + -15i2) = 0 Factor a trinomial. 3((2 + -5i)(2 + 3i)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(2 + -5i)' equal to zero and attempt to solve: Simplifying 2 + -5i = 0 Solving 2 + -5i = 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 + -5i = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5i = 0 + -2 -5i = 0 + -2 Combine like terms: 0 + -2 = -2 -5i = -2 Divide each side by '-5'. i = 0.4 Simplifying i = 0.4Subproblem 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 = {0.4, -0.6666666667}
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