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Simplifying (3 + -8i)(5 + i) = 0 Multiply (3 + -8i) * (5 + i) (3(5 + i) + -8i * (5 + i)) = 0 ((5 * 3 + i * 3) + -8i * (5 + i)) = 0 ((15 + 3i) + -8i * (5 + i)) = 0 (15 + 3i + (5 * -8i + i * -8i)) = 0 (15 + 3i + (-40i + -8i2)) = 0 Combine like terms: 3i + -40i = -37i (15 + -37i + -8i2) = 0 Solving 15 + -37i + -8i2 = 0 Solving for variable 'i'. Factor a trinomial. (3 + -8i)(5 + i) = 0Subproblem 1
Set the factor '(3 + -8i)' equal to zero and attempt to solve: Simplifying 3 + -8i = 0 Solving 3 + -8i = 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 + -8i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -8i = 0 + -3 -8i = 0 + -3 Combine like terms: 0 + -3 = -3 -8i = -3 Divide each side by '-8'. i = 0.375 Simplifying i = 0.375Subproblem 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 = {0.375, -5}
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