Q. The modulus and amplitude of $\frac{1 + 2i}{1 - (1 - i)^{2}}$ are
A) $\sqrt{2}\$ and $\frac{\pi}{6}$
B) 1 and 0
C) 1 and $\frac{\pi}{3}$
D) 1 and $\frac{\pi}{4}$
Explanation
(b)
Let $z = \frac{1 + 2i}{1 - (1 - i)^{2}} = 1$
$\therefore\ \ \ \ \ |z| = 1$ and $amp\ (z) = \tan^{- 1}\left( \frac{0}{1} \right) = 0$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.