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Simplifying (11 + -4i)(-5 + -9i) = 0 Multiply (11 + -4i) * (-5 + -9i) (11(-5 + -9i) + -4i * (-5 + -9i)) = 0 ((-5 * 11 + -9i * 11) + -4i * (-5 + -9i)) = 0 ((-55 + -99i) + -4i * (-5 + -9i)) = 0 (-55 + -99i + (-5 * -4i + -9i * -4i)) = 0 (-55 + -99i + (20i + 36i2)) = 0 Combine like terms: -99i + 20i = -79i (-55 + -79i + 36i2) = 0 Solving -55 + -79i + 36i2 = 0 Solving for variable 'i'. Factor a trinomial. (-5 + -9i)(11 + -4i) = 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 '(11 + -4i)' equal to zero and attempt to solve: Simplifying 11 + -4i = 0 Solving 11 + -4i = 0 Move all terms containing i to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -4i = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -4i = 0 + -11 -4i = 0 + -11 Combine like terms: 0 + -11 = -11 -4i = -11 Divide each side by '-4'. i = 2.75 Simplifying i = 2.75Solution
i = {-0.5555555556, 2.75}
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