For a non-zero complex number 
, let 
denote the principal argument with 
. Then, which of the following statement(s) is (are) FALSE? (JEE Advanced 2018)
, where 
, defined by 
for all 
, is continuous at all points of 
, where 
and 
, 
is an integer multiple of 
and 
, the locus of the point 
satisfying the condition 
, lies on a straight line
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
(a, b, d)
Complex number 
lies in third quadrant.
We have 
for all 
Complex number 
lies in second quadrant if 
and in third quadrant if 
.
Clearly, 
is discontinuous at 
.
Where 
and 
are angles subtended by line segment joining 
and 
at 
and 
respectively.
So, we get the following figure:
Thus, locus of 
is a circle.
──────────────────────────────────────────────────────────────────────────────────────────
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems