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Simplifying (5 + -4i)(8 + i) = 0 Multiply (5 + -4i) * (8 + i) (5(8 + i) + -4i * (8 + i)) = 0 ((8 * 5 + i * 5) + -4i * (8 + i)) = 0 ((40 + 5i) + -4i * (8 + i)) = 0 (40 + 5i + (8 * -4i + i * -4i)) = 0 (40 + 5i + (-32i + -4i2)) = 0 Combine like terms: 5i + -32i = -27i (40 + -27i + -4i2) = 0 Solving 40 + -27i + -4i2 = 0 Solving for variable 'i'. Factor a trinomial. (5 + -4i)(8 + i) = 0Subproblem 1
Set the factor '(5 + -4i)' equal to zero and attempt to solve: Simplifying 5 + -4i = 0 Solving 5 + -4i = 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 + -4i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4i = 0 + -5 -4i = 0 + -5 Combine like terms: 0 + -5 = -5 -4i = -5 Divide each side by '-4'. i = 1.25 Simplifying i = 1.25Subproblem 2
Set the factor '(8 + i)' equal to zero and attempt to solve: Simplifying 8 + i = 0 Solving 8 + i = 0 Move all terms containing i to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + i = 0 + -8 Combine like terms: 8 + -8 = 0 0 + i = 0 + -8 i = 0 + -8 Combine like terms: 0 + -8 = -8 i = -8 Simplifying i = -8Solution
i = {1.25, -8}
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