<p><strong>Theorem 1</strong></p>
<p>Let&nbsp;\(z\) be a complex number. Then</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">\(zz^* = |z|^2\).</span></div></li><li><div class="list-item-content"><span class="list-item-text">\((z + w)^* = z^* + w^*\).</span></div></li></ol>
<ol class="i-list" start="3"><li><div class="list-item-content"><span class="list-item-text">\((zw)^* = z^* w^*\).</span></div></li><li><div class="list-item-content"><span class="list-item-text">\(\left(\frac{z}{w}\right)^* = \frac{z^*}{w^*}\).</span></div></li><li><div class="list-item-content"><span class="list-item-text">\((z^n)^* = (z^*)^n\), where&nbsp;\(n \in \mathbb{Z}\).</span></div></li></ol>

\(\left(\frac{z}{w}\right)^* = \frac{z^*}{w^*}\).

\((z^n)^* = (z^*)^n\), where \(n \in \mathbb{Z}\).

Conjugate Complex Number

Complex Numbers

International Baccalaureate Higher Level Mathematics

Theorem on properties of conjugation

Theorem on properties of conjugation