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Simplifying (9 + -4i)(5 + i) = 0 Multiply (9 + -4i) * (5 + i) (9(5 + i) + -4i * (5 + i)) = 0 ((5 * 9 + i * 9) + -4i * (5 + i)) = 0 ((45 + 9i) + -4i * (5 + i)) = 0 (45 + 9i + (5 * -4i + i * -4i)) = 0 (45 + 9i + (-20i + -4i2)) = 0 Combine like terms: 9i + -20i = -11i (45 + -11i + -4i2) = 0 Solving 45 + -11i + -4i2 = 0 Solving for variable 'i'. Factor a trinomial. (9 + -4i)(5 + i) = 0Subproblem 1
Set the factor '(9 + -4i)' equal to zero and attempt to solve: Simplifying 9 + -4i = 0 Solving 9 + -4i = 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 + -4i = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -4i = 0 + -9 -4i = 0 + -9 Combine like terms: 0 + -9 = -9 -4i = -9 Divide each side by '-4'. i = 2.25 Simplifying i = 2.25Subproblem 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 = {2.25, -5}
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