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NDA Math Complex Numbers
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© examsnet.com
Question : 13
Total: 66
If
Z
=
1
+
i
, where
i
=
√
−
1
, then what is the modulus of
z
+
2
z
?
[NDA-I 2021]
1
2
3
4
Validate
Solution:
👈: Video Solution
Concept:
i
2
=
−
1
Calculation:
z
=
1
+
i
z
+
2
Z
=
1
+
i
+
2
1
+
i
On rationalizing,
=
1
+
i
+
2
1
+
i
×
1
−
i
1
−
i
=
1
+
i
+
2
×
(
1
−
i
)
1
−
i
2
=
1
+
i
+
2
×
(
1
−
i
)
1
−
(
−
1
)
=
1
+
i
+
2
×
(
1
−
i
)
2
=
1
+
i
+
1
−
i
=
2
So, the modulus of
z
+
2
z
=
2
© examsnet.com
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