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UPSC NDA 2 2016 Mathematics Solved Paper
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© examsnet.com
Question : 6
Total: 120
If
R
e
(
z
−
1
z
+
1
)
=
0
,where
2
=
x
+
i
y
is a can pi ex number, then which one of the following is correct?
[NDA II 2016]
z
=
1
+
i
|
z
|
=
2
z
=
1
−
i
|
z
|
=
1
Validate
Solution:
z
−
1
z
+
1
=
x
+
i
y
−
1
x
+
i
y
+
1
z
−
1
z
+
1
=
x
2
+
y
2
−
1
+
2
i
y
x
2
+
y
2
+
2
x
+
1
⇒
R
e
(
z
−
1
z
+
1
)
=
x
2
+
y
2
−
1
x
2
+
y
2
+
2
x
+
1
=
0
⇒
x
2
+
y
2
−
1
=
0
⇒
x
2
+
y
2
=
1
Also,
z
z
=
x
2
+
y
2
=
1
and
z
z
=
|
z
|
2
⇒
|
z
|
2
=
1
⇒
|
z
|
=
1
© examsnet.com
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