Published by:
CGP EDU Academic Team
Published on: August 12, 2026
Consider the complex numbers 
and 
satisfying the relation 
.
(i) Complex number 
is
A
purely real purely real 
0
0
B
purely imaginary
purely imaginary
purely imaginary
C
zero zero 0 
D
none of these (ii) Complex number 
is
none of these (iii) One of the possible argument of complex number
none of these (iv) Possible difference between the argument of
and 
is
none of these
is none of these (iii) One of the possible argument of complex number
none of these (iv) Possible difference between the argument of
and is none of these
Text Solution
Verified by ExpertsThe correct answer is:
A
(i) , (ii) , (iii) , (iv)
Given that
……… . (i)
(dividing by 
)
……… (ii)
From (i), 
is purely imaginary. From (ii), 
is purely imaginary. Hence,
Also, 
is purely real. Hence its possible arguments are 0 and 
.
──────────────────────────────────────────────────────────────────────────────────────────
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
The locus of the points representing the complex numbers z for which |z| – 2 = 0, |z – i| – |z + 5i…
If , then-
If and , then is equal to
Show that the equation Z 4 + 2Z 3 + 3Z 2 + 4Z + 5 = 0 has no root which is either purely real or pu…
Consider the locus of the complex number in the Argand plane is given by 2 i. Let and be two co…
Find the mirror image of the curve about the line .