Complex Numbers And Quadratic Equations question 372
Question: If the amplitude of $ z-2-3i $ is $ \pi /4 $ , then the locus of $ z=x+iy $ is [EAMCET 2003]
Options:
A) $ x+y-1=0 $
B) $ x-y-1=0 $
C) $ x+y+1=0 $
D) $ x-y+1=0 $
Show Answer
Answer:
Correct Answer: D
Solution:
$ z-2-3i=x+iy-2-3i=(x-2)+i(y-3) $ $ {{\tan }^{-1}}( \frac{y-3}{x-2} )=\frac{\pi }{4}\Rightarrow \frac{y-3}{x-2}=\tan \frac{\pi }{4}=1 $
Þ $ x-y+1=0. $
BETA
