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Byju's Answer
Standard XII
Mathematics
Sum of Infinite Terms
For two compl...
Question
For two complex numbers z and w it is given that (|z|^2)w — (|w|^2)z = z —w holds. Then show that either z=w or zw* =1 where w* is the conjugate of w.
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Q.
For complex numbers
z
and
w
,prove that
|
z
|
2
w
−
|
w
|
2
z
=
z
−
w
if and only if
z
=
w
or
z
¯
w
=
1
.
Q.
If z and w be two complex numbers, such that
|
z
|
2
w
−
|
w
|
2
z
=
z
−
w
and
(
z
≠
w
)
,
then
Q.
If
Z
and
W
are two complex numbers such that
¯
z
+
i
¯
w
=
0
and
a
r
g
(
z
w
)
=
π
then
a
r
g
(
Z
)
=
____________
Q.
If
z
and
w
be two complex numbers such that
|
z
|
≤
1
,
|
w
|
≤
1
and
|
z
+
i
w
|
=
|
z
−
i
¯
¯¯
¯
w
|
=
2
,
then
Q.
If
z
and
w
are two complex numbers such that
|
z
w
|
=
1
and
a
r
g
(
z
)
−
a
r
g
(
w
)
=
π
2
, then
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