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Simplifying (-8 + -9i)(5 + -1i) = 0 Multiply (-8 + -9i) * (5 + -1i) (-8(5 + -1i) + -9i * (5 + -1i)) = 0 ((5 * -8 + -1i * -8) + -9i * (5 + -1i)) = 0 ((-40 + 8i) + -9i * (5 + -1i)) = 0 (-40 + 8i + (5 * -9i + -1i * -9i)) = 0 (-40 + 8i + (-45i + 9i2)) = 0 Combine like terms: 8i + -45i = -37i (-40 + -37i + 9i2) = 0 Solving -40 + -37i + 9i2 = 0 Solving for variable 'i'. Factor a trinomial. (-8 + -9i)(5 + -1i) = 0Subproblem 1
Set the factor '(-8 + -9i)' equal to zero and attempt to solve: Simplifying -8 + -9i = 0 Solving -8 + -9i = 0 Move all terms containing i to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -9i = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -9i = 0 + 8 -9i = 0 + 8 Combine like terms: 0 + 8 = 8 -9i = 8 Divide each side by '-9'. i = -0.8888888889 Simplifying i = -0.8888888889Subproblem 2
Set the factor '(5 + -1i)' equal to zero and attempt to solve: Simplifying 5 + -1i = 0 Solving 5 + -1i = 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 + -1i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1i = 0 + -5 -1i = 0 + -5 Combine like terms: 0 + -5 = -5 -1i = -5 Divide each side by '-1'. i = 5 Simplifying i = 5Solution
i = {-0.8888888889, 5}
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