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Simplifying (-3 + 2i)(-3 + -4i) = 0 Multiply (-3 + 2i) * (-3 + -4i) (-3(-3 + -4i) + 2i * (-3 + -4i)) = 0 ((-3 * -3 + -4i * -3) + 2i * (-3 + -4i)) = 0 ((9 + 12i) + 2i * (-3 + -4i)) = 0 (9 + 12i + (-3 * 2i + -4i * 2i)) = 0 (9 + 12i + (-6i + -8i2)) = 0 Combine like terms: 12i + -6i = 6i (9 + 6i + -8i2) = 0 Solving 9 + 6i + -8i2 = 0 Solving for variable 'i'. Factor a trinomial. (3 + -2i)(3 + 4i) = 0Subproblem 1
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 = 1.5Subproblem 2
Set the factor '(3 + 4i)' equal to zero and attempt to solve: Simplifying 3 + 4i = 0 Solving 3 + 4i = 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 + 4i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 4i = 0 + -3 4i = 0 + -3 Combine like terms: 0 + -3 = -3 4i = -3 Divide each side by '4'. i = -0.75 Simplifying i = -0.75Solution
i = {1.5, -0.75}
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