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Simplifying (5 + -8i)(6 + i) = 0 Multiply (5 + -8i) * (6 + i) (5(6 + i) + -8i * (6 + i)) = 0 ((6 * 5 + i * 5) + -8i * (6 + i)) = 0 ((30 + 5i) + -8i * (6 + i)) = 0 (30 + 5i + (6 * -8i + i * -8i)) = 0 (30 + 5i + (-48i + -8i2)) = 0 Combine like terms: 5i + -48i = -43i (30 + -43i + -8i2) = 0 Solving 30 + -43i + -8i2 = 0 Solving for variable 'i'. Factor a trinomial. (5 + -8i)(6 + i) = 0Subproblem 1
Set the factor '(5 + -8i)' equal to zero and attempt to solve: Simplifying 5 + -8i = 0 Solving 5 + -8i = 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 + -8i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -8i = 0 + -5 -8i = 0 + -5 Combine like terms: 0 + -5 = -5 -8i = -5 Divide each side by '-8'. i = 0.625 Simplifying i = 0.625Subproblem 2
Set the factor '(6 + i)' equal to zero and attempt to solve: Simplifying 6 + i = 0 Solving 6 + i = 0 Move all terms containing i to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + i = 0 + -6 Combine like terms: 6 + -6 = 0 0 + i = 0 + -6 i = 0 + -6 Combine like terms: 0 + -6 = -6 i = -6 Simplifying i = -6Solution
i = {0.625, -6}
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