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Simplifying (2i + 3)(3i + 7) = 0 Reorder the terms: (3 + 2i)(3i + 7) = 0 Reorder the terms: (3 + 2i)(7 + 3i) = 0 Multiply (3 + 2i) * (7 + 3i) (3(7 + 3i) + 2i * (7 + 3i)) = 0 ((7 * 3 + 3i * 3) + 2i * (7 + 3i)) = 0 ((21 + 9i) + 2i * (7 + 3i)) = 0 (21 + 9i + (7 * 2i + 3i * 2i)) = 0 (21 + 9i + (14i + 6i2)) = 0 Combine like terms: 9i + 14i = 23i (21 + 23i + 6i2) = 0 Solving 21 + 23i + 6i2 = 0 Solving for variable 'i'. Factor a trinomial. (7 + 3i)(3 + 2i) = 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 '(3 + 2i)' equal to zero and attempt to solve: Simplifying 3 + 2i = 0 Solving 3 + 2i = 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 + 2i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2i = 0 + -3 2i = 0 + -3 Combine like terms: 0 + -3 = -3 2i = -3 Divide each side by '2'. i = -1.5 Simplifying i = -1.5Solution
i = {-2.333333333, -1.5}
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