Complex Numbers And Quadratic Equations question 84
Question: $ arg(5-\sqrt{3}i)= $
Options:
A) $ {{\tan }^{-1}}\frac{5}{\sqrt{3}} $
B) $ {{\tan }^{-1}}( -\frac{5}{\sqrt{3}} ) $
C) $ {{\tan }^{-1}}\frac{\sqrt{3}}{5} $
D) $ {{\tan }^{-1}}( -\frac{\sqrt{3}}{5} ) $
Show Answer
Answer:
Correct Answer: D
Solution:
Let $ z=5-\sqrt{3}i $
Þ $ r(\cos \theta +i\sin \theta )=5-\sqrt{3}i $
Þ $ r\cos \theta =5 $ and $ r\sin \theta =-\sqrt{3} $
$ \therefore $ $ \tan \theta =-\frac{\sqrt{3}}{5}\Rightarrow \theta ={{\tan }^{-1}}( -\frac{\sqrt{3}}{5} ) $
BETA
