Complex Numbers And Quadratic Equations question 103

Question: If $ 0<amp\text{ (z)}<\pi \text{,} $ then amp $ (z) $ - amp $ (-z)= $

Options:

A) 0

B) $ 2amp(z) $

C) $ \pi $

D) $ -\pi $

Show Answer

Answer:

Correct Answer: C

Solution:

amp(z) $ -amp(-z)={{\tan }^{-1}}\frac{y}{x}-( {{\tan }^{-1}}\frac{y}{x}-\pi )=\pi $