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AP EAPCET 07-Jul-2022 Shift 2 Paper
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© examsnet.com
Question : 8
Total: 160
Let
z
and
w
be two distinct non-zero complex numbers if
|
z
|
2
w
−
|
w
|
2
z
=
z
−
w
, then
w
=
z
2
z
w
=
2
z
w
=
1
w
=
z
Validate
Solution:
👈: Video Solution
(
|
z
|
2
+
1
)
w
=
(
|
w
|
2
+
1
)
z
.
.
.
[
Given
]
∴ Let
z
=
k
w
,
k
≠
1
,
k
≠
0
∴
k
2
|
w
|
2
w
−
k
|
w
|
2
w
=
k
w
−
w
∴
k
|
w
|
2
w
(
k
−
1
)
=
(
k
−
1
)
w
⇒
k
=
1
|
w
|
2
∴
z
=
w
|
w
|
2
z
w
=
w
|
w
|
2
⋅
w
=
|
w
|
2
|
w
|
2
=
1
© examsnet.com
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