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Simplifying (1 + i)(i + 2) = 0 Reorder the terms: (1 + i)(2 + i) = 0 Multiply (1 + i) * (2 + i) (1(2 + i) + i(2 + i)) = 0 ((2 * 1 + i * 1) + i(2 + i)) = 0 ((2 + 1i) + i(2 + i)) = 0 (2 + 1i + (2 * i + i * i)) = 0 (2 + 1i + (2i + i2)) = 0 Combine like terms: 1i + 2i = 3i (2 + 3i + i2) = 0 Solving 2 + 3i + i2 = 0 Solving for variable 'i'. Factor a trinomial. (2 + i)(1 + i) = 0Subproblem 1
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 = -2Subproblem 2
Set the factor '(1 + i)' equal to zero and attempt to solve: Simplifying 1 + i = 0 Solving 1 + i = 0 Move all terms containing i to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + i = 0 + -1 i = 0 + -1 Combine like terms: 0 + -1 = -1 i = -1 Simplifying i = -1Solution
i = {-2, -1}
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