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Simplifying (5 + -8i)(9 + i) = 0 Multiply (5 + -8i) * (9 + i) (5(9 + i) + -8i * (9 + i)) = 0 ((9 * 5 + i * 5) + -8i * (9 + i)) = 0 ((45 + 5i) + -8i * (9 + i)) = 0 (45 + 5i + (9 * -8i + i * -8i)) = 0 (45 + 5i + (-72i + -8i2)) = 0 Combine like terms: 5i + -72i = -67i (45 + -67i + -8i2) = 0 Solving 45 + -67i + -8i2 = 0 Solving for variable 'i'. Factor a trinomial. (5 + -8i)(9 + 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 '(9 + i)' equal to zero and attempt to solve: Simplifying 9 + i = 0 Solving 9 + i = 0 Move all terms containing i to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + i = 0 + -9 Combine like terms: 9 + -9 = 0 0 + i = 0 + -9 i = 0 + -9 Combine like terms: 0 + -9 = -9 i = -9 Simplifying i = -9Solution
i = {0.625, -9}
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