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Simplifying (3i + 5)(i + 7) = 0 Reorder the terms: (5 + 3i)(i + 7) = 0 Reorder the terms: (5 + 3i)(7 + i) = 0 Multiply (5 + 3i) * (7 + i) (5(7 + i) + 3i * (7 + i)) = 0 ((7 * 5 + i * 5) + 3i * (7 + i)) = 0 ((35 + 5i) + 3i * (7 + i)) = 0 (35 + 5i + (7 * 3i + i * 3i)) = 0 (35 + 5i + (21i + 3i2)) = 0 Combine like terms: 5i + 21i = 26i (35 + 26i + 3i2) = 0 Solving 35 + 26i + 3i2 = 0 Solving for variable 'i'. Factor a trinomial. (7 + i)(5 + 3i) = 0Subproblem 1
Set the factor '(7 + i)' equal to zero and attempt to solve: Simplifying 7 + i = 0 Solving 7 + i = 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 + i = 0 + -7 Combine like terms: 7 + -7 = 0 0 + i = 0 + -7 i = 0 + -7 Combine like terms: 0 + -7 = -7 i = -7 Simplifying i = -7Subproblem 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 = {-7, -1.666666667}
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