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Simplifying (3 + -2i)(-5 + -9i) = 0 Multiply (3 + -2i) * (-5 + -9i) (3(-5 + -9i) + -2i * (-5 + -9i)) = 0 ((-5 * 3 + -9i * 3) + -2i * (-5 + -9i)) = 0 ((-15 + -27i) + -2i * (-5 + -9i)) = 0 (-15 + -27i + (-5 * -2i + -9i * -2i)) = 0 (-15 + -27i + (10i + 18i2)) = 0 Combine like terms: -27i + 10i = -17i (-15 + -17i + 18i2) = 0 Solving -15 + -17i + 18i2 = 0 Solving for variable 'i'. Factor a trinomial. (-5 + -9i)(3 + -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 '(3 + -2i)' equal to zero and attempt to solve: Simplifying 3 + -2i = 0 Solving 3 + -2i = 0 Move all terms containing i to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -2i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2i = 0 + -3 -2i = 0 + -3 Combine like terms: 0 + -3 = -3 -2i = -3 Divide each side by '-2'. i = 1.5 Simplifying i = 1.5Solution
i = {-0.5555555556, 1.5}
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