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Simplifying (4 + -8i)(-5 + 4i) = 0 Multiply (4 + -8i) * (-5 + 4i) (4(-5 + 4i) + -8i * (-5 + 4i)) = 0 ((-5 * 4 + 4i * 4) + -8i * (-5 + 4i)) = 0 ((-20 + 16i) + -8i * (-5 + 4i)) = 0 (-20 + 16i + (-5 * -8i + 4i * -8i)) = 0 (-20 + 16i + (40i + -32i2)) = 0 Combine like terms: 16i + 40i = 56i (-20 + 56i + -32i2) = 0 Solving -20 + 56i + -32i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '4'. 4(-5 + 14i + -8i2) = 0 Factor a trinomial. 4((-5 + 4i)(1 + -2i)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-5 + 4i)' equal to zero and attempt to solve: Simplifying -5 + 4i = 0 Solving -5 + 4i = 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 + 4i = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 4i = 0 + 5 4i = 0 + 5 Combine like terms: 0 + 5 = 5 4i = 5 Divide each side by '4'. i = 1.25 Simplifying i = 1.25Subproblem 2
Set the factor '(1 + -2i)' equal to zero and attempt to solve: Simplifying 1 + -2i = 0 Solving 1 + -2i = 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 + -2i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2i = 0 + -1 -2i = 0 + -1 Combine like terms: 0 + -1 = -1 -2i = -1 Divide each side by '-2'. i = 0.5 Simplifying i = 0.5Solution
i = {1.25, 0.5}
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