<html><head><meta name="color-scheme" content="light dark"></head><body><pre style="word-wrap: break-word; white-space: pre-wrap;">\documentclass[a4paper,12pt]{article}
\newcommand\ds{\displaystyle}
\begin{document}

\parindent=0pt

QUESTION

Write $z=1-j$ in exponential form.

\bigskip


ANSWER

\setlength{\unitlength}{.5in}

\begin{picture}(4,4)

\put(2,0){\vector(0,1){4}}

\put(0,2){\vector(1,0){4}}

\put(2.2,1.8){$\alpha$}

\put(1.7,.9){-1}

\put(3,2.1){1}

\put(3.1,.9){$1-j$}

\put(2,1){\line(1,0){1}}

\put(3,1){\line(0,1){1}}

\put(2,2){\line(1,-1){1}}

\end{picture}

$\ds\tan \alpha=\frac{1}{1}=1,\ \alpha=\frac{\pi}{4},\
r=\sqrt{(1^2+(1)^2)}=\sqrt{2}$ therefore $\ds
1-j=\sqrt{2}e^{-j\frac{\pi}{4}}$





\end{document}
</pre></body></html>