The equation of the line through $2+3i$ which is perpendicular to the line through $0$ and $2+3i$ has equation \[az + b\overline{z} = 26,\]where $a$ and $b$ are constant complex numbers. Find the product $ab$ in rectangular form.
+26367 The equation of the line through $2+3i$ which is perpendicular to the line through $0$ and $2+3i$ has equation \[az + b\overline{z} = 26,\]
where $a$ and $b$ are constant complex numbers.
Find the product $ab$ in rectangular form.
\(\begin{array}{|rcll|} \hline az + b\overline{z} &=& 26 \\ &\boxed{ z = b} \\ & \boxed{\overline{z} = a} \\ ab + ba &=& 26 \\ 2ab &=& 26 \\ \mathbf{ab} &\mathbf{=}& \mathbf{13} \\ \hline \end{array}\)
