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Simplifying (5 + 2i)(3 + -5i) = 0 Multiply (5 + 2i) * (3 + -5i) (5(3 + -5i) + 2i * (3 + -5i)) = 0 ((3 * 5 + -5i * 5) + 2i * (3 + -5i)) = 0 ((15 + -25i) + 2i * (3 + -5i)) = 0 (15 + -25i + (3 * 2i + -5i * 2i)) = 0 (15 + -25i + (6i + -10i2)) = 0 Combine like terms: -25i + 6i = -19i (15 + -19i + -10i2) = 0 Solving 15 + -19i + -10i2 = 0 Solving for variable 'i'. Factor a trinomial. (3 + -5i)(5 + 2i) = 0Subproblem 1
Set the factor '(3 + -5i)' equal to zero and attempt to solve: Simplifying 3 + -5i = 0 Solving 3 + -5i = 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 + -5i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5i = 0 + -3 -5i = 0 + -3 Combine like terms: 0 + -3 = -3 -5i = -3 Divide each side by '-5'. i = 0.6 Simplifying i = 0.6Subproblem 2
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 = -2.5Solution
i = {0.6, -2.5}
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