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Simplifying (2 + i)(5 + i) = 0 Multiply (2 + i) * (5 + i) (2(5 + i) + i(5 + i)) = 0 ((5 * 2 + i * 2) + i(5 + i)) = 0 ((10 + 2i) + i(5 + i)) = 0 (10 + 2i + (5 * i + i * i)) = 0 (10 + 2i + (5i + i2)) = 0 Combine like terms: 2i + 5i = 7i (10 + 7i + i2) = 0 Solving 10 + 7i + i2 = 0 Solving for variable 'i'. Factor a trinomial. (5 + i)(2 + i) = 0Subproblem 1
Set the factor '(5 + i)' equal to zero and attempt to solve: Simplifying 5 + i = 0 Solving 5 + i = 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 + i = 0 + -5 Combine like terms: 5 + -5 = 0 0 + i = 0 + -5 i = 0 + -5 Combine like terms: 0 + -5 = -5 i = -5 Simplifying i = -5Subproblem 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 = {-5, -2}
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