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Simplifying (15 + -6i)(4 + 5i) = 0 Multiply (15 + -6i) * (4 + 5i) (15(4 + 5i) + -6i * (4 + 5i)) = 0 ((4 * 15 + 5i * 15) + -6i * (4 + 5i)) = 0 ((60 + 75i) + -6i * (4 + 5i)) = 0 (60 + 75i + (4 * -6i + 5i * -6i)) = 0 (60 + 75i + (-24i + -30i2)) = 0 Combine like terms: 75i + -24i = 51i (60 + 51i + -30i2) = 0 Solving 60 + 51i + -30i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '3'. 3(20 + 17i + -10i2) = 0 Factor a trinomial. 3((5 + -2i)(4 + 5i)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(5 + -2i)' equal to zero and attempt to solve: Simplifying 5 + -2i = 0 Solving 5 + -2i = 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 + -2i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2i = 0 + -5 -2i = 0 + -5 Combine like terms: 0 + -5 = -5 -2i = -5 Divide each side by '-2'. i = 2.5 Simplifying i = 2.5Subproblem 2
Set the factor '(4 + 5i)' equal to zero and attempt to solve: Simplifying 4 + 5i = 0 Solving 4 + 5i = 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 + 5i = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 5i = 0 + -4 5i = 0 + -4 Combine like terms: 0 + -4 = -4 5i = -4 Divide each side by '5'. i = -0.8 Simplifying i = -0.8Solution
i = {2.5, -0.8}
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