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Simplifying (5 + 2i)(5 + -9i) = 0 Multiply (5 + 2i) * (5 + -9i) (5(5 + -9i) + 2i * (5 + -9i)) = 0 ((5 * 5 + -9i * 5) + 2i * (5 + -9i)) = 0 ((25 + -45i) + 2i * (5 + -9i)) = 0 (25 + -45i + (5 * 2i + -9i * 2i)) = 0 (25 + -45i + (10i + -18i2)) = 0 Combine like terms: -45i + 10i = -35i (25 + -35i + -18i2) = 0 Solving 25 + -35i + -18i2 = 0 Solving for variable 'i'. Factor a trinomial. (5 + -9i)(5 + 2i) = 0Subproblem 1
Set the factor '(5 + -9i)' equal to zero and attempt to solve: Simplifying 5 + -9i = 0 Solving 5 + -9i = 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 + -9i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -9i = 0 + -5 -9i = 0 + -5 Combine like terms: 0 + -5 = -5 -9i = -5 Divide each side by '-9'. i = 0.5555555556 Simplifying i = 0.5555555556Subproblem 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 = {0.5555555556, -2.5}
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