<p>The complex number $w$ has modulus $\sqrt{2}$ and argument $-\frac{3\pi }{4}$, and the complex number $z$ has modulus $2$ and argument $-\frac{\pi }{3}$. Find the exact values of the modulus and argument of $wz$. By first expressing $w$ and $z$ in the form $x+y\mathbf{i}$, find the exact real and imaginary part of $wz$. Hence show that&nbsp;$\sin \frac{\pi }{12}=\frac{\sqrt{3}-1}{2\sqrt{2}}$ .</p>

The complex number $w$ has modulus $\sqrt{2}$ and argument $-\frac{3\pi }{4}$, and the complex number $z$ has modulus $2$ and argument $-\frac{\pi }{3}$. Find the exact values of the modulus and argument of $wz$. By first expressing $w$ and $z$ in the form $x+y\mathbf{i}$, find the exact real and imaginary part of $wz$. Hence show that $\sin \frac{\pi }{12}=\frac{\sqrt{3}-1}{2\sqrt{2}}$ .

Complex Numbers - General

Complex Numbers

International Baccalaureate Higher Level Mathematics

Complex Numbers - Complex Numbers - General

Complex Numbers - Complex Numbers - General