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Simplifying (5 + 9i)(5 + 9i) = 0 Multiply (5 + 9i) * (5 + 9i) (5(5 + 9i) + 9i * (5 + 9i)) = 0 ((5 * 5 + 9i * 5) + 9i * (5 + 9i)) = 0 ((25 + 45i) + 9i * (5 + 9i)) = 0 (25 + 45i + (5 * 9i + 9i * 9i)) = 0 (25 + 45i + (45i + 81i2)) = 0 Combine like terms: 45i + 45i = 90i (25 + 90i + 81i2) = 0 Solving 25 + 90i + 81i2 = 0 Solving for variable 'i'. Factor a trinomial. (5 + 9i)(5 + 9i) = 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 + 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 = {-0.5555555556, -0.5555555556}
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