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Byju's Answer
Standard XII
Mathematics
Conjugate of a Complex Number
If z1,z2,z3...
Question
If
z
1
,
z
2
,
z
3
are three distinct complex numbers and
p
,
q
,
r
are three positive real numbers such that
p
|
z
2
−
z
3
|
=
q
|
z
3
−
z
1
|
=
r
|
z
1
−
z
2
|
then
p
2
z
2
−
z
3
+
q
2
z
3
−
z
1
+
r
2
z
1
−
z
2
=
0
Open in App
Solution
p
2
=
k
2
|
z
2
−
z
3
|
2
=
k
2
(
z
2
−
z
3
)
(
¯
¯¯¯¯¯¯¯¯¯¯¯¯¯¯
¯
z
2
−
z
3
)
=
k
2
(
z
2
−
z
3
)
(
¯
¯¯¯¯¯¯¯¯¯¯¯¯¯¯
¯
z
2
−
z
3
)
∴
p
2
z
2
−
z
3
=
k
2
(
¯
z
2
−
¯
z
3
)
∴
∑
p
2
z
2
−
z
3
=
k
2
(
¯
z
2
−
¯
z
3
)
=
0
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0
Similar questions
Q.
State True=1 and False=0
If
z
1
,
z
2
,
z
3
are three distinct complex numbers and p, q, r are three positive real numbers such that
p
|
z
2
−
z
3
|
=
q
|
z
3
−
z
1
|
=
r
|
z
1
−
z
2
|
then
p
2
z
2
−
z
3
+
q
2
z
3
−
z
1
+
r
2
z
1
−
z
2
=
0
.
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 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
|
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
and
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 :
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