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Simplifying (3 + -5i)(8 + -2i) = 0 Multiply (3 + -5i) * (8 + -2i) (3(8 + -2i) + -5i * (8 + -2i)) = 0 ((8 * 3 + -2i * 3) + -5i * (8 + -2i)) = 0 ((24 + -6i) + -5i * (8 + -2i)) = 0 (24 + -6i + (8 * -5i + -2i * -5i)) = 0 (24 + -6i + (-40i + 10i2)) = 0 Combine like terms: -6i + -40i = -46i (24 + -46i + 10i2) = 0 Solving 24 + -46i + 10i2 = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '2'. 2(12 + -23i + 5i2) = 0 Factor a trinomial. 2((3 + -5i)(4 + -1i)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + -5i)' equal to zero and attempt to solve: Simplifying 3 + -5i = 0 Solving 3 + -5i = 0 Move all terms containing i to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -5i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5i = 0 + -3 -5i = 0 + -3 Combine like terms: 0 + -3 = -3 -5i = -3 Divide each side by '-5'. i = 0.6 Simplifying i = 0.6Subproblem 2
Set the factor '(4 + -1i)' equal to zero and attempt to solve: Simplifying 4 + -1i = 0 Solving 4 + -1i = 0 Move all terms containing i to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1i = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1i = 0 + -4 -1i = 0 + -4 Combine like terms: 0 + -4 = -4 -1i = -4 Divide each side by '-1'. i = 4 Simplifying i = 4Solution
i = {0.6, 4}
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