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Byju's Answer
Standard XII
Mathematics
Summation of Determinant
120. If |z1+z...
Question
120. If |z1+z2|=|z1|+|z2|,then proved that argument (z1)=argument (z2)
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Similar questions
Q.
If
|
z
1
+
z
2
|
=
|
z
1
−
z
2
|
then the difference between the arguments of
z
1
and
z
2
is:
Q.
If
z
1
,
z
2
∈
C
1
then prove that :
|
z
1
−
z
2
|
≥
|
z
z
|
−
|
z
2
|
Q.
If
z
1
and
z
2
are two complex numbers, then prove that
|
z
1
|
+
|
z
2
|
=
∣
∣
∣
z
1
+
z
2
2
+
√
z
1
z
2
∣
∣
∣
+
∣
∣
∣
z
1
+
z
2
2
−
√
z
1
z
2
∣
∣
∣
Q.
Consider the complex number
z
1
and
z
2
satisfying the relation
|
z
1
+
z
2
|
2
=
|
z
1
|
2
+
|
z
2
|
2
, then the p
ossible difference between the argument of
z
1
and
z
2
is,
Q.
(a) For any two non-zero complex numbers
z
1
and
z
2
if
|
z
1
+
z
2
|
=
|
z
1
|
+
|
z
2
|
, then prove that
a
r
g
z
1
−
a
r
g
z
2
is zero.
(b) Prove the above result if we have
|
z
1
−
z
2
|
=
|
z
1
|
−
|
z
2
|
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