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Simplifying (5 + 9i)(-5 + -2i) = 0 Multiply (5 + 9i) * (-5 + -2i) (5(-5 + -2i) + 9i * (-5 + -2i)) = 0 ((-5 * 5 + -2i * 5) + 9i * (-5 + -2i)) = 0 ((-25 + -10i) + 9i * (-5 + -2i)) = 0 (-25 + -10i + (-5 * 9i + -2i * 9i)) = 0 (-25 + -10i + (-45i + -18i2)) = 0 Combine like terms: -10i + -45i = -55i (-25 + -55i + -18i2) = 0 Solving -25 + -55i + -18i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '-1'. -1(25 + 55i + 18i2) = 0 Factor a trinomial. -1((5 + 2i)(5 + 9i)) = 0 Ignore the factor -1.Subproblem 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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