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Simplifying (3 + 2i)(9 + 5i) = 0 Multiply (3 + 2i) * (9 + 5i) (3(9 + 5i) + 2i * (9 + 5i)) = 0 ((9 * 3 + 5i * 3) + 2i * (9 + 5i)) = 0 ((27 + 15i) + 2i * (9 + 5i)) = 0 (27 + 15i + (9 * 2i + 5i * 2i)) = 0 (27 + 15i + (18i + 10i2)) = 0 Combine like terms: 15i + 18i = 33i (27 + 33i + 10i2) = 0 Solving 27 + 33i + 10i2 = 0 Solving for variable 'i'. Factor a trinomial. (9 + 5i)(3 + 2i) = 0Subproblem 1
Set the factor '(9 + 5i)' equal to zero and attempt to solve: Simplifying 9 + 5i = 0 Solving 9 + 5i = 0 Move all terms containing i to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + 5i = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 5i = 0 + -9 5i = 0 + -9 Combine like terms: 0 + -9 = -9 5i = -9 Divide each side by '5'. i = -1.8 Simplifying i = -1.8Subproblem 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 = {-1.8, -1.5}
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