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Simplifying (2 + -3i)(2 + i) = 0 Multiply (2 + -3i) * (2 + i) (2(2 + i) + -3i * (2 + i)) = 0 ((2 * 2 + i * 2) + -3i * (2 + i)) = 0 ((4 + 2i) + -3i * (2 + i)) = 0 (4 + 2i + (2 * -3i + i * -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 + -3i)(2 + i) = 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 '(2 + i)' equal to zero and attempt to solve: Simplifying 2 + i = 0 Solving 2 + i = 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 + i = 0 + -2 Combine like terms: 2 + -2 = 0 0 + i = 0 + -2 i = 0 + -2 Combine like terms: 0 + -2 = -2 i = -2 Simplifying i = -2Solution
i = {0.6666666667, -2}
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