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Simplifying (7 + 3i)(5 + 4i) = 0 Multiply (7 + 3i) * (5 + 4i) (7(5 + 4i) + 3i * (5 + 4i)) = 0 ((5 * 7 + 4i * 7) + 3i * (5 + 4i)) = 0 ((35 + 28i) + 3i * (5 + 4i)) = 0 (35 + 28i + (5 * 3i + 4i * 3i)) = 0 (35 + 28i + (15i + 12i2)) = 0 Combine like terms: 28i + 15i = 43i (35 + 43i + 12i2) = 0 Solving 35 + 43i + 12i2 = 0 Solving for variable 'i'. Factor a trinomial. (7 + 3i)(5 + 4i) = 0Subproblem 1
Set the factor '(7 + 3i)' equal to zero and attempt to solve: Simplifying 7 + 3i = 0 Solving 7 + 3i = 0 Move all terms containing i to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 3i = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 3i = 0 + -7 3i = 0 + -7 Combine like terms: 0 + -7 = -7 3i = -7 Divide each side by '3'. i = -2.333333333 Simplifying i = -2.333333333Subproblem 2
Set the factor '(5 + 4i)' equal to zero and attempt to solve: Simplifying 5 + 4i = 0 Solving 5 + 4i = 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 + 4i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 4i = 0 + -5 4i = 0 + -5 Combine like terms: 0 + -5 = -5 4i = -5 Divide each side by '4'. i = -1.25 Simplifying i = -1.25Solution
i = {-2.333333333, -1.25}
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