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Simplifying (5 + -2i)(4 + -1i) = 0 Multiply (5 + -2i) * (4 + -1i) (5(4 + -1i) + -2i * (4 + -1i)) = 0 ((4 * 5 + -1i * 5) + -2i * (4 + -1i)) = 0 ((20 + -5i) + -2i * (4 + -1i)) = 0 (20 + -5i + (4 * -2i + -1i * -2i)) = 0 (20 + -5i + (-8i + 2i2)) = 0 Combine like terms: -5i + -8i = -13i (20 + -13i + 2i2) = 0 Solving 20 + -13i + 2i2 = 0 Solving for variable 'i'. Factor a trinomial. (5 + -2i)(4 + -1i) = 0Subproblem 1
Set the factor '(5 + -2i)' equal to zero and attempt to solve: Simplifying 5 + -2i = 0 Solving 5 + -2i = 0 Move all terms containing i to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -2i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2i = 0 + -5 -2i = 0 + -5 Combine like terms: 0 + -5 = -5 -2i = -5 Divide each side by '-2'. i = 2.5 Simplifying i = 2.5Subproblem 2
Set the factor '(4 + -1i)' equal to zero and attempt to solve: Simplifying 4 + -1i = 0 Solving 4 + -1i = 0 Move all terms containing i to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1i = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1i = 0 + -4 -1i = 0 + -4 Combine like terms: 0 + -4 = -4 -1i = -4 Divide each side by '-1'. i = 4 Simplifying i = 4Solution
i = {2.5, 4}
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