Consider the line with equation \[(2-i)z + (2+i)\overline{z} = 20.\]
Where does this line intersect the real axis?
+26393 Consider the line with equation
\( (2-i)z + (2+i)\overline{z} = 20. \)
\[(2-i)z + (2+i)\overline{z} = 20.\]
Where does this line intersect the real axis?
On the real axis: \(z = \overline z\)
\(\begin{array}{|rcll|} \hline (2-i)z + (2+i)\overline{z} &=& 20 \quad & | \quad z = \overline z \\ (2-i)z + (2+i)z &=& 20 \\ z\Big((2-i)+(2+i)\Big) &=& 20 \\ z(2-i+2+i) &=& 20 \\ 4z &=& 20 \\ \mathbf{ z } & \mathbf{=} & \mathbf{5} \\ \hline \end{array}\)
The line intersect the real axis at 5.
