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NDA Math Complex Numbers
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© examsnet.com
Question : 45
Total: 66
If the point
z
1
=
1
+
i
where
i
=
√
−
1
is the reflection of a point
z
2
=
x
+
i
y
in the line
i
z
−
i
z
=
5
, then the point
z
2
is
[NDA II 2015]
1
+
4
i
4
+
i
1
−
i
−
1
−
i
Validate
Solution:
Let
z
=
a
+
b
i
⇒
−
z
=
a
−
b
i
∴
i
z
−
i
z
=
i
[
(
a
−
b
i
)
−
(
a
+
b
i
)
]
=
5
⇒
i
[
−
2
b
i
]
=
5
⇒
b
=
5
2
So from figure it is clear that
x
=
1
,
y
=
5
2
+
3
2
=
4
z
2
=
1
+
4
i
© examsnet.com
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