4 Fig. 4 shows the regular octagon ABCDEFGH .
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{a13f7a05-e2d3-4354-a0c7-ef7283eff514-05_689_696_301_239}
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\caption{Fig. 4}
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\(\overrightarrow { \mathrm { AB } } = \mathbf { i } , \overrightarrow { \mathrm { CD } } = \mathbf { j }\), where \(\mathbf { i }\) is a unit vector parallel to the \(x\)-axis and \(\mathbf { j }\) is a unit vector parallel to the \(y\)-axis.
Find an exact expression for \(\overrightarrow { \mathrm { BC } }\) in terms of \(\mathbf { i }\) and \(\mathbf { j }\).