PART III: MATHEMATICS
SECTION 1 (Maximum Marks: 18)
• This section contains SIX (06) questions.
• The answer to each question is a SINGLE DIGIT INTEGER ranging from 0 TO 9, BOTH INCLUSIVE.
• For each question, enter the correct integer corresponding to the answer using the mouse and the on-screen virtual numeric keypad in the place designated to enter the answer.
• Answer to each question will be evaluated according to the following marking scheme:
Full marks : +3 If ONL Y the correct integer is entered;
Zero Marks : 0 If the question is unanswered;
Negative Marks : -1 In all other cases.
For a complex number z, let Re(z) denote the real part of z. Let S be the set of all complex numbers z satisfying z 4 - |z| 4 = 4 i z 2 , where i = 
. Then the minimum possible value of |z 1 - z 2 | 2 , where z 1 , z 2 
S with Re(z 1 ) > 0 and Re(z 2 ) < 0, is_____
Text Solution
Verified by Experts8
(8)
z 4 - |z| 4 = 4i z 2 z
4 -z 2 - 
=4iz 2 
z
2 = 0 or z 2 - 
=4i
Let z = x + iy
(z + 
)(z- 
) = 4i
2x.2iy = 4i
xy= 1
z 1 lies on xy = 1 in first quadrant and z 2 lies on xy = 1 in third quadrant.
|z 1 - z 2 | 2 is minimum when z 1 = (1, 1) and z 2 = (-1, -1)
|z 1 - z 2 | 2 = 8
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