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Simplifying (2 + 5i)(4 + -1i) = 0 Multiply (2 + 5i) * (4 + -1i) (2(4 + -1i) + 5i * (4 + -1i)) = 0 ((4 * 2 + -1i * 2) + 5i * (4 + -1i)) = 0 ((8 + -2i) + 5i * (4 + -1i)) = 0 (8 + -2i + (4 * 5i + -1i * 5i)) = 0 (8 + -2i + (20i + -5i2)) = 0 Combine like terms: -2i + 20i = 18i (8 + 18i + -5i2) = 0 Solving 8 + 18i + -5i2 = 0 Solving for variable 'i'. Factor a trinomial. (4 + -1i)(2 + 5i) = 0Subproblem 1
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 = 4Subproblem 2
Set the factor '(2 + 5i)' equal to zero and attempt to solve: Simplifying 2 + 5i = 0 Solving 2 + 5i = 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 + 5i = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 5i = 0 + -2 5i = 0 + -2 Combine like terms: 0 + -2 = -2 5i = -2 Divide each side by '5'. i = -0.4 Simplifying i = -0.4Solution
i = {4, -0.4}
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