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Simplifying (3 + 6i)(7 + 2i) = 0 Multiply (3 + 6i) * (7 + 2i) (3(7 + 2i) + 6i * (7 + 2i)) = 0 ((7 * 3 + 2i * 3) + 6i * (7 + 2i)) = 0 ((21 + 6i) + 6i * (7 + 2i)) = 0 (21 + 6i + (7 * 6i + 2i * 6i)) = 0 (21 + 6i + (42i + 12i2)) = 0 Combine like terms: 6i + 42i = 48i (21 + 48i + 12i2) = 0 Solving 21 + 48i + 12i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '3'. 3(7 + 16i + 4i2) = 0 Factor a trinomial. 3((7 + 2i)(1 + 2i)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(7 + 2i)' equal to zero and attempt to solve: Simplifying 7 + 2i = 0 Solving 7 + 2i = 0 Move all terms containing i to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 2i = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 2i = 0 + -7 2i = 0 + -7 Combine like terms: 0 + -7 = -7 2i = -7 Divide each side by '2'. i = -3.5 Simplifying i = -3.5Subproblem 2
Set the factor '(1 + 2i)' equal to zero and attempt to solve: Simplifying 1 + 2i = 0 Solving 1 + 2i = 0 Move all terms containing i to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2i = 0 + -1 2i = 0 + -1 Combine like terms: 0 + -1 = -1 2i = -1 Divide each side by '2'. i = -0.5 Simplifying i = -0.5Solution
i = {-3.5, -0.5}
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