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Simplifying (5 + i)(4 + -2i) = 0 Multiply (5 + i) * (4 + -2i) (5(4 + -2i) + i(4 + -2i)) = 0 ((4 * 5 + -2i * 5) + i(4 + -2i)) = 0 ((20 + -10i) + i(4 + -2i)) = 0 (20 + -10i + (4 * i + -2i * i)) = 0 (20 + -10i + (4i + -2i2)) = 0 Combine like terms: -10i + 4i = -6i (20 + -6i + -2i2) = 0 Solving 20 + -6i + -2i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '2'. 2(10 + -3i + -1i2) = 0 Factor a trinomial. 2((2 + -1i)(5 + i)) = 0 Ignore the factor 2.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 + 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 = {2, -5}
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