<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">Simplify \(i^{19}\), \(i^{30}\) and \(i^{-672}\).</span></div></li><li><div class="list-item-content"><span class="list-item-text">Evaluate \(i^{1+2+3+\dots+15}\).</span></div></li><li><div class="list-item-content"><span class="list-item-text">Simplify \(\left(\frac{1+i}{1-i}\right)^{4n+2} + \left(\frac{1-i}{1+i}\right)^{4n+1}\), where&nbsp;\(n\) is a positive integer.</span></div></li></ol>

Simplify \(i^{19}\), \(i^{30}\) and \(i^{-672}\).

Simplify \(\left(\frac{1+i}{1-i}\right)^{4n+2} + \left(\frac{1-i}{1+i}\right)^{4n+1}\), where \(n\) is a positive integer.

Complex Numbers - General

Complex Numbers

International Baccalaureate Higher Level Mathematics

Powers of complex numbers

Powers of complex numbers