Cho số phức \(z=x+yi\). Tìm phầ...

B

- Hướng dẫn giải

Ta có: 
\(z = x + yi \Rightarrow \bar z = x - yi \)

\(\Rightarrow w = \frac{{\bar z + i}}{{iz - 1}} = \frac{{x + \left( {1 - y} \right)i}}{{i\left( {x + yi} \right) - 1}}\)

\(\begin{array}{*{20}{l}}
{ \Rightarrow w = \frac{{x + \left( {1 - y} \right)i}}{{ - y - 1 + xi}} = \frac{{\left[ {x + \left( {1 - y} \right)i} \right]\left( {y + 1 + xi} \right)}}{{{{\left( {xi} \right)}^2} - {{\left( {y + 1} \right)}^2}}}}\\
{ = \frac{{x\left( {y + 1} \right) - x\left( {1 - y} \right) + \left( {{x^2} - {y^2} + 1} \right)i}}{{ - {x^2} - {{\left( {y + 1} \right)}^2}}}}\\
{ =  - \frac{{2xy}}{{{x^2} + {{\left( {y + 1} \right)}^2}}} + \frac{{{y^2} - {x^2} - 1}}{{{x^2} + {{\left( {y + 1} \right)}^2}}}i}
\end{array}\)