Complex Numbers And Quadratic Equations question 840
Question: The imaginary part of $ {{\tan }^{-1}}( \frac{5i}{3} ) $ is [RPET 1997]
Options:
A) 0
B) $ \infty $
C) $ \log 2 $
D) $ \log 4 $
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Answer:
Correct Answer: C
Solution:
$ {{\tan }^{-1}}( \frac{5i}{3} )=i{{\tan }^{-1}}( \frac{5}{3} )=\frac{i}{2}\log ( \frac{\frac{5}{3}+1}{\frac{5}{3}-1} ) $ $ Im( {{\tan }^{-1}}( \frac{5i}{3} ) )=\frac{1}{2}\log 4=\frac{1}{2}.2\log 2=\log 2 $ .
BETA
