1
You visited us
1
times! Enjoying our articles?
Unlock Full Access!
Byju's Answer
Standard XII
Mathematics
Modulus of a Complex Number
If |z| ≤ 1,...
Question
If
|
z
|
≤
1
,
|
w
|
≤
1
, then
|
z
−
w
|
2
≤
(
|
z
|
−
|
w
|
)
2
+
(
a
r
g
z
−
a
r
g
w
)
2
. If this is true enter 1, else enter 0.
Open in App
Solution
From the figure
α
=
(
a
r
g
z
−
a
r
g
ω
)
....... (1)
and
s
i
n
2
α
/
2
≤
(
α
/
2
)
2
...... (2)
In
Δ
OAB, from cosine rule
(
A
B
)
2
=
(
O
a
)
2
+
(
O
B
)
2
−
2
O
A
.
O
B
c
o
s
α
⇒
|
z
−
ω
|
2
=
|
z
|
2
+
|
ω
|
2
−
2
|
z
|
|
ω
|
c
o
s
α
⇒
|
z
−
ω
|
2
=
(
|
z
|
−
|
ω
|
)
2
+
2
|
z
|
|
ω
|
(
1
−
c
o
s
α
)
⇒
|
z
−
ω
|
2
=
(
|
z
|
−
|
ω
|
)
2
+
4
|
z
|
|
ω
|
s
i
n
2
α
/
2
⇒
|
z
−
ω
|
2
≤
(
|
z
|
−
|
ω
|
)
2
+
|
z
|
|
ω
|
α
2
[from (2)]
⇒
|
z
−
ω
|
2
≤
(
|
z
|
−
|
ω
|
)
2
+
α
2
{
∵
|
z
|
≤
1
,
|
ω
|
≤
1
}
|
z
−
ω
|
2
≤
(
|
z
|
−
|
ω
|
)
2
+
(
a
r
g
z
−
a
r
g
ω
)
2
{from (1)}
Ans: 1
Suggest Corrections
0
Similar questions
Q.
If
|
z
|
≤
1
,
|
w
|
≤
1
show that
|
z
−
w
|
2
≤
(
|
z
|
−
|
w
|
)
2
=
(
A
r
g
z
−
A
r
g
w
)
2
Q.
If
i
z
3
+
z
2
−
z
+
i
=
0
, then
|
z
|
=
1
. If this is true enter 1, else enter 0.
Q.
If Arg
(
z
+
i
)
−
Arg
(
z
−
i
)
=
π
2
, then
z
lies on a circle.
If statement is True, enter
1
, else enter
0
Q.
If
|
z
|
≤
1
,
|
w
|
≤
1
,
then
Q.
If
z
and
w
be two complex numbers such that
|
z
|
≤
1
,
|
w
|
≤
1
and
|
z
+
i
w
|
=
|
z
−
i
¯
¯¯
¯
w
|
=
2
,
then
View More
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
Related Videos
Geometric Representation and Trigonometric Form
MATHEMATICS
Watch in App
Explore more
Modulus of a Complex Number
Standard XII Mathematics
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
AI Tutor
Textbooks
Question Papers
Install app