Question

Convert the following complex numbers into polar form.
$\frac{(\sqrt{3}-1)-(\sqrt{3}+1)i}{2\sqrt{2}}$

• A. $e^{i\frac{\pi }{12}}$
• B. $e^{-i\frac{13\pi }{12}}$
• C. $e^{-i\frac{\pi }{12}}$
• D. $e^{-i\frac{\pi }{6}}$

Answer 1

Answer: (A)

$e^{i\frac{\pi }{12}}$

$\frac{\sqrt{3}-1-(\sqrt{3}+1)i}{2\sqrt{2}}$

$=\frac{\sqrt{3}-1}{2\sqrt{2}}-\frac{(\sqrt{3}+1)}{2\sqrt{2}}i$

$=x-iy$

$\propto =-\theta$

$=\cos (-\frac{\pi }{12})+i\sin \left(\frac{\pi }{12}\right)$

$=e^{-\frac{i\pi }{12}}$.