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Simplifying (-5 + -1i)(-2 + 4i) = 0 Multiply (-5 + -1i) * (-2 + 4i) (-5(-2 + 4i) + -1i * (-2 + 4i)) = 0 ((-2 * -5 + 4i * -5) + -1i * (-2 + 4i)) = 0 ((10 + -20i) + -1i * (-2 + 4i)) = 0 (10 + -20i + (-2 * -1i + 4i * -1i)) = 0 (10 + -20i + (2i + -4i2)) = 0 Combine like terms: -20i + 2i = -18i (10 + -18i + -4i2) = 0 Solving 10 + -18i + -4i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '2'. 2(5 + -9i + -2i2) = 0 Factor a trinomial. 2((1 + -2i)(5 + i)) = 0 Ignore the factor 2.Subproblem 1
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 = 0.5Subproblem 2
Set the factor '(5 + i)' equal to zero and attempt to solve: Simplifying 5 + i = 0 Solving 5 + i = 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 + i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + i = 0 + -5 i = 0 + -5 Combine like terms: 0 + -5 = -5 i = -5 Simplifying i = -5Solution
i = {0.5, -5}
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