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Simplifying (2 + i)(1 + 2i) = 0 Multiply (2 + i) * (1 + 2i) (2(1 + 2i) + i(1 + 2i)) = 0 ((1 * 2 + 2i * 2) + i(1 + 2i)) = 0 ((2 + 4i) + i(1 + 2i)) = 0 (2 + 4i + (1 * i + 2i * i)) = 0 (2 + 4i + (1i + 2i2)) = 0 Combine like terms: 4i + 1i = 5i (2 + 5i + 2i2) = 0 Solving 2 + 5i + 2i2 = 0 Solving for variable 'i'. Factor a trinomial. (2 + i)(1 + 2i) = 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 + 2i)' equal to zero and attempt to solve: Simplifying 1 + 2i = 0 Solving 1 + 2i = 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 + 2i = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2i = 0 + -1 2i = 0 + -1 Combine like terms: 0 + -1 = -1 2i = -1 Divide each side by '2'. i = -0.5 Simplifying i = -0.5Solution
i = {-2, -0.5}
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