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WBJEE 2018 Math Solved Paper
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© examsnet.com
Question : 48
Total: 75
If
z
1
and
z
2
be two non zero complex numbers such that
z
1
z
2
+
z
2
z
1
=
1
, then the origin and the points represented by
z
1
and
z
2
lie on a straight line
form a right angled triangle
form an equilateral triangle
form an isosceles triangle
Validate
Solution:
z
1
=
z
2
e
i
π
/
3
2
z
1
=
z
2
(
1
+
i
√
3
)
2
z
1
−
z
2
=
i
√
3
z
2
⇒
4
z
1
2
+
z
2
2
−
4
z
1
z
2
=
−
3
z
2
2
⇒
4
z
1
2
+
4
z
2
2
=
4
z
1
z
2
Hence form equilateral triangle.
© examsnet.com
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