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Simplifying (9 + 5i)(-5 + 9i) = 0 Multiply (9 + 5i) * (-5 + 9i) (9(-5 + 9i) + 5i * (-5 + 9i)) = 0 ((-5 * 9 + 9i * 9) + 5i * (-5 + 9i)) = 0 ((-45 + 81i) + 5i * (-5 + 9i)) = 0 (-45 + 81i + (-5 * 5i + 9i * 5i)) = 0 (-45 + 81i + (-25i + 45i2)) = 0 Combine like terms: 81i + -25i = 56i (-45 + 56i + 45i2) = 0 Solving -45 + 56i + 45i2 = 0 Solving for variable 'i'. Factor a trinomial. (-9 + -5i)(5 + -9i) = 0Subproblem 1
Set the factor '(-9 + -5i)' equal to zero and attempt to solve: Simplifying -9 + -5i = 0 Solving -9 + -5i = 0 Move all terms containing i to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -5i = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -5i = 0 + 9 -5i = 0 + 9 Combine like terms: 0 + 9 = 9 -5i = 9 Divide each side by '-5'. i = -1.8 Simplifying i = -1.8Subproblem 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 = {-1.8, 0.5555555556}
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