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Simplifying (6 + 3i)(5 + 2i) = 0 Multiply (6 + 3i) * (5 + 2i) (6(5 + 2i) + 3i * (5 + 2i)) = 0 ((5 * 6 + 2i * 6) + 3i * (5 + 2i)) = 0 ((30 + 12i) + 3i * (5 + 2i)) = 0 (30 + 12i + (5 * 3i + 2i * 3i)) = 0 (30 + 12i + (15i + 6i2)) = 0 Combine like terms: 12i + 15i = 27i (30 + 27i + 6i2) = 0 Solving 30 + 27i + 6i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '3'. 3(10 + 9i + 2i2) = 0 Factor a trinomial. 3((5 + 2i)(2 + i)) = 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 '(2 + i)' equal to zero and attempt to solve: Simplifying 2 + i = 0 Solving 2 + i = 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 + i = 0 + -2 Combine like terms: 2 + -2 = 0 0 + i = 0 + -2 i = 0 + -2 Combine like terms: 0 + -2 = -2 i = -2 Simplifying i = -2Solution
i = {-2.5, -2}
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