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Simplifying (5 + -8i)(-4 + -4i) = 0 Multiply (5 + -8i) * (-4 + -4i) (5(-4 + -4i) + -8i * (-4 + -4i)) = 0 ((-4 * 5 + -4i * 5) + -8i * (-4 + -4i)) = 0 ((-20 + -20i) + -8i * (-4 + -4i)) = 0 (-20 + -20i + (-4 * -8i + -4i * -8i)) = 0 (-20 + -20i + (32i + 32i2)) = 0 Combine like terms: -20i + 32i = 12i (-20 + 12i + 32i2) = 0 Solving -20 + 12i + 32i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '4'. 4(-5 + 3i + 8i2) = 0 Factor a trinomial. 4((-1 + -1i)(5 + -8i)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-1 + -1i)' equal to zero and attempt to solve: Simplifying -1 + -1i = 0 Solving -1 + -1i = 0 Move all terms containing i to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1i = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1i = 0 + 1 -1i = 0 + 1 Combine like terms: 0 + 1 = 1 -1i = 1 Divide each side by '-1'. i = -1 Simplifying i = -1Subproblem 2
Set the factor '(5 + -8i)' equal to zero and attempt to solve: Simplifying 5 + -8i = 0 Solving 5 + -8i = 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 + -8i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -8i = 0 + -5 -8i = 0 + -5 Combine like terms: 0 + -5 = -5 -8i = -5 Divide each side by '-8'. i = 0.625 Simplifying i = 0.625Solution
i = {-1, 0.625}
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