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TS EAMCET 7 May 2018 Shift 1 Solved Paper
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© examsnet.com
Question : 9
Total: 160
If z = x + iy is a complex number and |1 + iz| = |1 - iz| , then
Re (z) > 0
|z| = 1
z =
−
z
z = -
−
z
Validate
Solution:
Given:
z
=
x
+
i
y
a complex number,
|
1
+
i
z
|
=
|
1
−
i
z
|
|
1
+
i
(
x
+
i
y
)
|
=
|
1
−
i
(
x
+
i
y
)
|
|
1
−
y
+
x
i
|
=
|
1
+
y
−
i
x
|
(
1
−
y
)
2
+
x
2
=
(
1
+
y
)
2
+
x
2
(
1
−
y
)
=
(
1
+
y
)
2
y
=
0
y
=
0
Now,
z
=
x
+
i
y
z
=
x
+
i
0
z
=
x
And
z
=
x
∴
z
=
z
© examsnet.com
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