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Simplifying (3 + 4i)(5 + 2i) = 0 Multiply (3 + 4i) * (5 + 2i) (3(5 + 2i) + 4i * (5 + 2i)) = 0 ((5 * 3 + 2i * 3) + 4i * (5 + 2i)) = 0 ((15 + 6i) + 4i * (5 + 2i)) = 0 (15 + 6i + (5 * 4i + 2i * 4i)) = 0 (15 + 6i + (20i + 8i2)) = 0 Combine like terms: 6i + 20i = 26i (15 + 26i + 8i2) = 0 Solving 15 + 26i + 8i2 = 0 Solving for variable 'i'. Factor a trinomial. (5 + 2i)(3 + 4i) = 0Subproblem 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 '(3 + 4i)' equal to zero and attempt to solve: Simplifying 3 + 4i = 0 Solving 3 + 4i = 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 + 4i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4i = 0 + -3 4i = 0 + -3 Combine like terms: 0 + -3 = -3 4i = -3 Divide each side by '4'. i = -0.75 Simplifying i = -0.75Solution
i = {-2.5, -0.75}
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