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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 + -2i)(5 + 9i) = 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 '(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 = -0.5555555556Solution
i = {2.5, -0.5555555556}
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