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Simplifying (2i + -3)(3i + -2) = 0 Reorder the terms: (-3 + 2i)(3i + -2) = 0 Reorder the terms: (-3 + 2i)(-2 + 3i) = 0 Multiply (-3 + 2i) * (-2 + 3i) (-3(-2 + 3i) + 2i * (-2 + 3i)) = 0 ((-2 * -3 + 3i * -3) + 2i * (-2 + 3i)) = 0 ((6 + -9i) + 2i * (-2 + 3i)) = 0 (6 + -9i + (-2 * 2i + 3i * 2i)) = 0 (6 + -9i + (-4i + 6i2)) = 0 Combine like terms: -9i + -4i = -13i (6 + -13i + 6i2) = 0 Solving 6 + -13i + 6i2 = 0 Solving for variable 'i'. Factor a trinomial. (2 + -3i)(3 + -2i) = 0Subproblem 1
Set the factor '(2 + -3i)' equal to zero and attempt to solve: Simplifying 2 + -3i = 0 Solving 2 + -3i = 0 Move all terms containing i to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3i = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3i = 0 + -2 -3i = 0 + -2 Combine like terms: 0 + -2 = -2 -3i = -2 Divide each side by '-3'. i = 0.6666666667 Simplifying i = 0.6666666667Subproblem 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 = {0.6666666667, 1.5}
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