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Simplifying (-8 + -4i)(5 + -6i) = 0 Multiply (-8 + -4i) * (5 + -6i) (-8(5 + -6i) + -4i * (5 + -6i)) = 0 ((5 * -8 + -6i * -8) + -4i * (5 + -6i)) = 0 ((-40 + 48i) + -4i * (5 + -6i)) = 0 (-40 + 48i + (5 * -4i + -6i * -4i)) = 0 (-40 + 48i + (-20i + 24i2)) = 0 Combine like terms: 48i + -20i = 28i (-40 + 28i + 24i2) = 0 Solving -40 + 28i + 24i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '4'. 4(-10 + 7i + 6i2) = 0 Factor a trinomial. 4((-2 + -1i)(5 + -6i)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-2 + -1i)' equal to zero and attempt to solve: Simplifying -2 + -1i = 0 Solving -2 + -1i = 0 Move all terms containing i to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1i = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1i = 0 + 2 -1i = 0 + 2 Combine like terms: 0 + 2 = 2 -1i = 2 Divide each side by '-1'. i = -2 Simplifying i = -2Subproblem 2
Set the factor '(5 + -6i)' equal to zero and attempt to solve: Simplifying 5 + -6i = 0 Solving 5 + -6i = 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 + -6i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -6i = 0 + -5 -6i = 0 + -5 Combine like terms: 0 + -5 = -5 -6i = -5 Divide each side by '-6'. i = 0.8333333333 Simplifying i = 0.8333333333Solution
i = {-2, 0.8333333333}
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