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Simplifying (3 + 7i)(5 + i) = 0 Multiply (3 + 7i) * (5 + i) (3(5 + i) + 7i * (5 + i)) = 0 ((5 * 3 + i * 3) + 7i * (5 + i)) = 0 ((15 + 3i) + 7i * (5 + i)) = 0 (15 + 3i + (5 * 7i + i * 7i)) = 0 (15 + 3i + (35i + 7i2)) = 0 Combine like terms: 3i + 35i = 38i (15 + 38i + 7i2) = 0 Solving 15 + 38i + 7i2 = 0 Solving for variable 'i'. Factor a trinomial. (5 + i)(3 + 7i) = 0Subproblem 1
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 = -5Subproblem 2
Set the factor '(3 + 7i)' equal to zero and attempt to solve: Simplifying 3 + 7i = 0 Solving 3 + 7i = 0 Move all terms containing i to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 7i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 7i = 0 + -3 7i = 0 + -3 Combine like terms: 0 + -3 = -3 7i = -3 Divide each side by '7'. i = -0.4285714286 Simplifying i = -0.4285714286Solution
i = {-5, -0.4285714286}
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