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Simplifying (3 + 7i)(4 + 3i) = 0 Multiply (3 + 7i) * (4 + 3i) (3(4 + 3i) + 7i * (4 + 3i)) = 0 ((4 * 3 + 3i * 3) + 7i * (4 + 3i)) = 0 ((12 + 9i) + 7i * (4 + 3i)) = 0 (12 + 9i + (4 * 7i + 3i * 7i)) = 0 (12 + 9i + (28i + 21i2)) = 0 Combine like terms: 9i + 28i = 37i (12 + 37i + 21i2) = 0 Solving 12 + 37i + 21i2 = 0 Solving for variable 'i'. Factor a trinomial. (4 + 3i)(3 + 7i) = 0Subproblem 1
Set the factor '(4 + 3i)' equal to zero and attempt to solve: Simplifying 4 + 3i = 0 Solving 4 + 3i = 0 Move all terms containing i to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + 3i = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 3i = 0 + -4 3i = 0 + -4 Combine like terms: 0 + -4 = -4 3i = -4 Divide each side by '3'. i = -1.333333333 Simplifying i = -1.333333333Subproblem 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 = {-1.333333333, -0.4285714286}
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