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# The equation of the line through $2+3i$ which is perpendicular to the line through $0$ and $2+3i$ has equation $az + b\overline{z} = 26,$w

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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.

Jan 18, 2019

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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.

$$\begin{array}{|rcll|} \hline az + b\overline{z} &=& 26 \\ &\boxed{ z = b} \\ & \boxed{\overline{z} = a} \\ ab + ba &=& 26 \\ 2ab &=& 26 \\ \mathbf{ab} &\mathbf{=}& \mathbf{13} \\ \hline \end{array}$$

Jan 18, 2019