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Simplifying (9 + i)(5 + -3i) = 0 Multiply (9 + i) * (5 + -3i) (9(5 + -3i) + i(5 + -3i)) = 0 ((5 * 9 + -3i * 9) + i(5 + -3i)) = 0 ((45 + -27i) + i(5 + -3i)) = 0 (45 + -27i + (5 * i + -3i * i)) = 0 (45 + -27i + (5i + -3i2)) = 0 Combine like terms: -27i + 5i = -22i (45 + -22i + -3i2) = 0 Solving 45 + -22i + -3i2 = 0 Solving for variable 'i'. Factor a trinomial. (5 + -3i)(9 + i) = 0Subproblem 1
Set the factor '(5 + -3i)' equal to zero and attempt to solve: Simplifying 5 + -3i = 0 Solving 5 + -3i = 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 + -3i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3i = 0 + -5 -3i = 0 + -5 Combine like terms: 0 + -5 = -5 -3i = -5 Divide each side by '-3'. i = 1.666666667 Simplifying i = 1.666666667Subproblem 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 = {1.666666667, -9}
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