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Simplifying (2 + 3i)(2 + -1i) = 0 Multiply (2 + 3i) * (2 + -1i) (2(2 + -1i) + 3i * (2 + -1i)) = 0 ((2 * 2 + -1i * 2) + 3i * (2 + -1i)) = 0 ((4 + -2i) + 3i * (2 + -1i)) = 0 (4 + -2i + (2 * 3i + -1i * 3i)) = 0 (4 + -2i + (6i + -3i2)) = 0 Combine like terms: -2i + 6i = 4i (4 + 4i + -3i2) = 0 Solving 4 + 4i + -3i2 = 0 Solving for variable 'i'. Factor a trinomial. (2 + -1i)(2 + 3i) = 0Subproblem 1
Set the factor '(2 + -1i)' equal to zero and attempt to solve: Simplifying 2 + -1i = 0 Solving 2 + -1i = 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 + -1i = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1i = 0 + -2 -1i = 0 + -2 Combine like terms: 0 + -2 = -2 -1i = -2 Divide each side by '-1'. i = 2 Simplifying i = 2Subproblem 2
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 = -0.6666666667Solution
i = {2, -0.6666666667}
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