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Simplifying (15)(5 + -4i)(3 + 2i) = 0 Multiply (5 + -4i) * (3 + 2i) 15(5(3 + 2i) + -4i * (3 + 2i)) = 0 15((3 * 5 + 2i * 5) + -4i * (3 + 2i)) = 0 15((15 + 10i) + -4i * (3 + 2i)) = 0 15(15 + 10i + (3 * -4i + 2i * -4i)) = 0 15(15 + 10i + (-12i + -8i2)) = 0 Combine like terms: 10i + -12i = -2i 15(15 + -2i + -8i2) = 0 (15 * 15 + -2i * 15 + -8i2 * 15) = 0 (225 + -30i + -120i2) = 0 Solving 225 + -30i + -120i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '15'. 15(15 + -2i + -8i2) = 0 Factor a trinomial. 15((5 + -4i)(3 + 2i)) = 0 Ignore the factor 15.Subproblem 1
Set the factor '(5 + -4i)' equal to zero and attempt to solve: Simplifying 5 + -4i = 0 Solving 5 + -4i = 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 + -4i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4i = 0 + -5 -4i = 0 + -5 Combine like terms: 0 + -5 = -5 -4i = -5 Divide each side by '-4'. i = 1.25 Simplifying i = 1.25Subproblem 2
Set the factor '(3 + 2i)' equal to zero and attempt to solve: Simplifying 3 + 2i = 0 Solving 3 + 2i = 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 + 2i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2i = 0 + -3 2i = 0 + -3 Combine like terms: 0 + -3 = -3 2i = -3 Divide each side by '2'. i = -1.5 Simplifying i = -1.5Solution
i = {1.25, -1.5}
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