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Byju's Answer
Standard VI
Mathematics
Identifying Shaded Fractions
Q. nbsp; ...
Question
Q.
z
1
and
z
2
are two complex numbers such that
z
1
-
2
z
2
2
-
z
1
z
2
¯
is unimodular whereas
z
2
is not a unimodular.
Then |
z
1
| is
1
2
3
4
Open in App
Solution
Dear student
A
complex
number
z
is
said
to
be
unimodular
if
|
z
|
=
1
.
Consider
,
z
1
-
2
z
2
2
-
z
1
z
2
Since
z
1
-
2
z
2
2
-
z
1
z
2
is
unimodular
then
z
1
-
2
z
2
2
-
z
1
z
2
=
1
⇒
|
z
1
-
2
z
2
|
=
|
2
-
z
1
z
2
|
⇒
|
z
1
-
2
z
2
|
2
=
|
2
-
z
1
z
2
|
2
⇒
z
1
-
2
z
2
z
1
-
2
z
2
=
2
-
z
1
z
2
2
-
z
1
z
2
using
z
2
=
z
z
⇒
z
1
z
1
-
2
z
1
z
2
-
2
z
2
z
1
+
4
z
2
z
2
=
4
-
2
z
1
z
2
-
2
z
1
z
2
+
z
1
z
1
z
2
z
2
⇒
z
1
2
+
4
z
2
2
=
4
+
z
1
2
z
2
2
⇒
z
1
2
+
4
z
2
2
-
4
-
z
1
2
z
2
2
=
0
⇒
z
1
2
1
-
z
2
2
-
4
1
-
z
2
2
=
0
⇒
1
-
z
2
2
z
1
2
-
4
=
0
Since
z
2
≠
1
⇒
z
1
2
-
4
=
0
⇒
z
1
2
=
4
⇒
z
1
=
2
Regards
Suggest Corrections
0
Similar questions
Q.
A complex number
z
is said to be unimodular if
|
z
|
=
1
. Suppose
z
1
and
z
2
are complex numbers such that
z
1
−
2
z
2
2
−
z
1
¯
¯
¯
z
2
is unimodular and
z
2
is not unimodular. Then the point
z
1
lies on a
Q.
z
1
and
z
2
are complex numbers such that
z
1
−
2
z
2
2
−
z
1
¯
z
2
is unimodular and Z2 is not unimodular. Find
|
z
1
|
Q.
Let
z
1
and
z
2
be two complex numbers such that
z
1
−
3
z
2
3
−
z
1
¯
¯
¯
z
2
is unimodular. If
z
2
is not unimodular then
|
z
1
|
is
Q.
Assertion :
If
z
1
≠
z
2
and
|
z
1
+
z
2
|
=
∣
∣
∣
1
z
1
+
1
z
2
∣
∣
∣
then
z
1
z
2
is unimodular.
Reason: Both
z
1
and
z
2
are unimodular.
Q.
State whether the following statement is true or false.
Let
z
1
,
z
2
be two complex numbers such that
z
1
−
2
z
2
2
−
z
2
¯
z
2
is unimodular. If
z
2
is not unimodular then
|
z
1
|
=
2
.
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