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      <text>23.6.2.1 Revision of the exponential form of a complex number</text>
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      <text><![CDATA[<h4>Revision of the exponential form of a complex number</h4>

Recall that a complex number in <b>Cartesian</b> form which is written as
\[z = a + ib \]
where \(a\) and \(b\) are real numbers and \(i^2 = -1\), can be written in <b>polar</b> form as
\[ z = r \left( \cos \theta + i \sin \theta \right) \]
where \(r = \lvert z \rvert =\sqrt{a^2 + b^2} \) and \(\theta\), the <b>argument</b> or <b>phase</b> of \(z\) is such that
\[ a = r \cos \theta \hspace{1cm} b = r \sin \theta \]
A more concise version of the polar form of \(z\) can be obtained by defining a <b>complex exponential</b>
quantity \(e^{i\theta}\) by Euler's relation
\[ e^{i\theta} \equiv \cos \theta + i \sin \theta \]
The polar angle \(\theta\) is normally expressed in <b>radians</b>. Replacing i by \( - i\) we obtain the alternative form
\[ e^{-i\theta} \equiv \cos \theta - i \sin \theta \]]]></text>
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