Complex Numbers And Quadratic Equations question 121
Question: The modulus and amplitude of $ \frac{1+2i}{1-{{(1-i)}^{2}}} $ are [Karnataka CET 2005]
Options:
A) $ \sqrt{2}\text{ and }\frac{\pi }{6} $
B) 1 and 0
C) 1 and $ \frac{\pi }{3} $
D) 1 and $ \frac{\pi }{4} $
Show Answer
Answer:
Correct Answer: B
Solution:
$ \frac{1+2i}{1-{{(1-i)}^{2}}}=\frac{1+2i}{1-(1-1-2i)}=\frac{1+2i}{1+2i}=1+0i $ Modulus =1 Amplitude $ \theta $ = $ {{\tan }^{-1}}\frac{0}{1}=0 $ .
BETA
