Complex Numbers And Quadratic Equations question 145
Question: Let $ z,w $ be complex numbers such that $ \overline{z}+i\overline{w}=0 $ and $ argzw=\pi $ . Then arg z equals [AIEEE 2004]
Options:
A) $ 5\pi /4 $
B) $ \pi /2 $
C) $ 3\pi /4 $
D) $ \pi /4 $
Show Answer
Answer:
Correct Answer: C
Solution:
Given that arg zw = $ \pi $ …..(i) $ \bar{z}+i\bar{\omega }=0\Rightarrow \bar{z}=-i\bar{\omega } $
$ \Rightarrow z=i\omega $
$ \Rightarrow \omega =-iz $ From (i), arg $ (-iz^{2})=\pi $ $ arg\ (-i)+2arg(z)=\pi $ ; $ \frac{-\pi }{2}+2\ arg(z)=\pi $ $ 2arg(z)=\frac{3\pi }{2} $ ; $ arg(z)=\frac{3\pi }{4} $
BETA
