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Byju's Answer
Standard X
Mathematics
Cartesian Product
Let z1,z2 and...
Question
Let z1,z2 and z3 be 3 distinct complex no.s.If |z1|=|z2|=|z3|=1 ,then prove that |(z1 z2)+(z2 z3)+(z1 z3)|=|z1+z2+z3|
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Q.
If
z
1
,
z
2
and
z
3
are three distinct complex numbers such that
1
∣
z
1
−
z
2
∣
=
3
∣
z
2
−
z
3
∣
=
5
∣
z
1
−
z
3
∣
, then the value of
1
z
1
−
z
2
+
9
z
2
−
z
3
+
25
z
3
−
z
1
is
Q.
If
z
1
,
z
2
,
z
3
are
3
distinct complex numbers such that
3
|
z
2
−
z
3
|
=
4
|
z
3
−
z
1
|
=
5
|
z
1
−
z
2
|
, then the value of
9
z
2
−
z
3
+
16
z
3
−
z
1
+
25
z
1
−
z
2
equals
Q.
If
z
1
,
z
2
,
z
3
be complex number such that
|
z
1
|
=
|
z
2
|
=
|
z
3
|
=
∣
∣
1
z
1
+
1
z
2
+
1
z
3
∣
∣
= 1 then
|
z
1
+
z
2
+
z
3
|
is
Q.
If
z
1
,
z
2
,
z
3
are complex numbers such that
|
z
1
|
=
|
z
2
|
=
|
z
3
|
=
∣
∣
∣
1
z
1
+
1
z
2
+
1
z
3
∣
∣
∣
=
1
, then
|
z
1
+
z
2
+
z
3
|
is:
Q.
If
z
1
,
z
2
,
z
3
are complex number such that
|
z
1
|
=
|
z
2
|
=
|
z
3
|
∣
∣
∣
1
z
1
+
1
z
2
+
1
z
3
∣
∣
∣
=
1
,
then
|
z
1
+
z
2
+
z
3
|
is
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