复数 z=frac{1}{2+i} (其中 i 为虚数单位) 的虚部为

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Step:1 ：First, we multiply the numerator and denominator by the conjugate of the denominator, which is 2-i.Step:2 ：(z = frac{1}{2+i} times frac{2-i}{2-i})Step:3 ：(z = frac{2-i}{(2+i)(2-i)})Step:4 ：(z = frac{2-i}{2^2 + i^2})Step:5 ：(z = frac{2-i}{4 - 1})Step:6 ：(z = frac{2-i}{3})Step:7 ：Finally, the imaginary part of the complex number z=frac{1}{2+i} is (boxed{-frac{1}{3}})

Answer

Step: 1 ：First, we multiply the numerator and denominator by the conjugate of the denominator, which is 2-i.Step: 2 ：(z = frac{1}{2+i} times frac{2-i}{2-i})Step: 3 ：(z = frac{2-i}{(2+i)(2-i)})Step: 4 ：(z = frac{2-i}{2^2 + i^2})Step: 5 ：(z = frac{2-i}{4 - 1})Step: 6 ：(z = frac{2-i}{3})Step: 7 ：Finally, the imaginary part of the complex number z=frac{1}{2+i} is (boxed{-frac{1}{3}})

复数 $z=\frac{1}{2+i}$ (其中 $i$ 为虚数单位) 的虚部为

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