Complex Numbers And Quadratic Equations question 469
Question: If z and $ \omega $ are two non-zero complex numbers such that $ | z |=| \omega | $ and arg z + arg $ \omega $ = $ \pi $ , then z equals
Options:
A) $ \bar{\omega } $
B) - $ \bar{\omega } $
C) $ \omega $
D) - $ \omega $
Show Answer
Answer:
Correct Answer: B
Solution:
[b] Let $ | z |=| \omega |=r $
$ \therefore z=r{e^{i\theta }},\omega =r{e^{i\theta }} $ Where $ \theta +\phi =\pi $
$ \therefore \overline{\omega }=r{e^{-i\phi }} $
$ \therefore z=r{e^{i(\pi -\phi )}}=r{e^{i\pi }}{e^{-i\phi }}=r{{-e}^{-i\phi }}=-\overline{\omega } $
BETA
