For any two complex numbers 
and 
,
and equality holds if origin 
and 
are collinear and 
lie on the same side of the origin.
(i) If 
and sum of greatest and least values of 
is 
, then 
is equal to ………
(ii) If 
and sum of greatest and least values of 
is 
, then 
is equal to………
Text Solution
Verified by Experts(i) (24); (ii) (12)
(i) (24)
If 
, where 
.......(i)
Also, 
Case I 
Case II 
From Case I and Case II, we get
.........(ii)
From Eqs. (i) and (ii), we get
The greatest value of 
is 
and the least value of 
is 
.
Here, 
and 
Sum of the greatest and least value of 
.
(ii) (12)
If 
, where 
.......(i)
Also, 
Case I 
Case II 
From Case I and Case II, we get
.........(ii)
From Eqs. (i) and (ii), we get
The greatest value of 
is 
and the least value of 
is 
.
Here, 
and 
Sum of the greatest and least value of 
──────────────────────────────────────────────────────────────────────────────────────────
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