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Simplifying (5 + 3i)(9 + -4i) = 0 Multiply (5 + 3i) * (9 + -4i) (5(9 + -4i) + 3i * (9 + -4i)) = 0 ((9 * 5 + -4i * 5) + 3i * (9 + -4i)) = 0 ((45 + -20i) + 3i * (9 + -4i)) = 0 (45 + -20i + (9 * 3i + -4i * 3i)) = 0 (45 + -20i + (27i + -12i2)) = 0 Combine like terms: -20i + 27i = 7i (45 + 7i + -12i2) = 0 Solving 45 + 7i + -12i2 = 0 Solving for variable 'i'. Factor a trinomial. (9 + -4i)(5 + 3i) = 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 + 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 = -1.666666667Solution
i = {2.25, -1.666666667}
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