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Simplifying (5 + -1i)(-2 + -8i) = 0 Multiply (5 + -1i) * (-2 + -8i) (5(-2 + -8i) + -1i * (-2 + -8i)) = 0 ((-2 * 5 + -8i * 5) + -1i * (-2 + -8i)) = 0 ((-10 + -40i) + -1i * (-2 + -8i)) = 0 (-10 + -40i + (-2 * -1i + -8i * -1i)) = 0 (-10 + -40i + (2i + 8i2)) = 0 Combine like terms: -40i + 2i = -38i (-10 + -38i + 8i2) = 0 Solving -10 + -38i + 8i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + -19i + 4i2) = 0 Factor a trinomial. 2((-1 + -4i)(5 + -1i)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + -4i)' equal to zero and attempt to solve: Simplifying -1 + -4i = 0 Solving -1 + -4i = 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 + -4i = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -4i = 0 + 1 -4i = 0 + 1 Combine like terms: 0 + 1 = 1 -4i = 1 Divide each side by '-4'. i = -0.25 Simplifying i = -0.25Subproblem 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 = {-0.25, 5}
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