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UPSC NDA I 2021 Mathematics Solved Paper
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© examsnet.com
Question : 24
Total: 120
Consider the following in respect of a complex number z:
1.
(
z
−
1
)
=
(
z
)
−
1
2.
z
z
−
1
=
|
z
|
2
Which of the above is/are correct?
[NDA-I 2021]
1 only
2 only
Both 1 and 2
Neither 1 nor 2
Validate
Solution:
👈: Video Solution
Concept
Consider
z
=
a
+
i
b
Multiplicative identity
z
⋅
z
−
1
=
1
z
z
=
a
2
+
b
2
=
(
a
+
i
b
)
(
a
−
i
b
)
Explanation
Given:
1
⋅
(
z
−
1
)
=
(
z
)
−
1
consider
z
=
a
−
i
b
z
−
1
=
a
−
i
b
a
2
+
b
2
.
.
.
.
(
1
)
z
=
a
+
i
b
(
z
)
−
1
=
1
z
=
1
a
+
i
b
=
a
−
i
b
a
2
+
b
2
from eq(1) and (2)
statement 1 is correct. 2.
z
z
−
1
=
|
z
|
2
consider
z
=
a
−
i
b
z
−
1
=
a
+
i
b
a
2
+
b
2
z
⋅
z
−
1
=
(
a
−
i
b
)
a
+
i
b
a
2
+
b
2
=
a
2
+
b
2
a
2
+
b
2
=
1
Statement 2 is not correct
© examsnet.com
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