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Simplifying (9 + -3i)(4 + 5i) = 0 Multiply (9 + -3i) * (4 + 5i) (9(4 + 5i) + -3i * (4 + 5i)) = 0 ((4 * 9 + 5i * 9) + -3i * (4 + 5i)) = 0 ((36 + 45i) + -3i * (4 + 5i)) = 0 (36 + 45i + (4 * -3i + 5i * -3i)) = 0 (36 + 45i + (-12i + -15i2)) = 0 Combine like terms: 45i + -12i = 33i (36 + 33i + -15i2) = 0 Solving 36 + 33i + -15i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '3'. 3(12 + 11i + -5i2) = 0 Factor a trinomial. 3((3 + -1i)(4 + 5i)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(3 + -1i)' equal to zero and attempt to solve: Simplifying 3 + -1i = 0 Solving 3 + -1i = 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 + -1i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1i = 0 + -3 -1i = 0 + -3 Combine like terms: 0 + -3 = -3 -1i = -3 Divide each side by '-1'. i = 3 Simplifying i = 3Subproblem 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 = {3, -0.8}
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