Question

show that:

If $r=\cos \theta +i\sin \theta$ then $|r-1/r|=2\sin \theta$. If this is true enter 1, else enter 0.

Answer 1

given that $r=\cos \theta +i\sin \theta$

$\therefore \frac{1}{r}=\cos \theta -i\sin \theta$
now $|r-1/r|=|(\cos \theta +i\sin \theta )-(\cos \theta -i\sin \theta )|=\left|2i\sin \theta \right|=2\sin \theta$
Ans: 1