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Simplifying (8 + i)(2 + 7i) = 0 Multiply (8 + i) * (2 + 7i) (8(2 + 7i) + i(2 + 7i)) = 0 ((2 * 8 + 7i * 8) + i(2 + 7i)) = 0 ((16 + 56i) + i(2 + 7i)) = 0 (16 + 56i + (2 * i + 7i * i)) = 0 (16 + 56i + (2i + 7i2)) = 0 Combine like terms: 56i + 2i = 58i (16 + 58i + 7i2) = 0 Solving 16 + 58i + 7i2 = 0 Solving for variable 'i'. Factor a trinomial. (8 + i)(2 + 7i) = 0Subproblem 1
Set the factor '(8 + i)' equal to zero and attempt to solve: Simplifying 8 + i = 0 Solving 8 + i = 0 Move all terms containing i to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + i = 0 + -8 Combine like terms: 8 + -8 = 0 0 + i = 0 + -8 i = 0 + -8 Combine like terms: 0 + -8 = -8 i = -8 Simplifying i = -8Subproblem 2
Set the factor '(2 + 7i)' equal to zero and attempt to solve: Simplifying 2 + 7i = 0 Solving 2 + 7i = 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 + 7i = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 7i = 0 + -2 7i = 0 + -2 Combine like terms: 0 + -2 = -2 7i = -2 Divide each side by '7'. i = -0.2857142857 Simplifying i = -0.2857142857Solution
i = {-8, -0.2857142857}
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