1
You visited us
1
times! Enjoying our articles?
Unlock Full Access!
Byju's Answer
Standard XI
Mathematics
Euler's Representation
If tanα+iβ=ei...
Question
If
tan
(
α
+
i
β
)
=
e
i
θ
;
where
α
,
β
∈
R
,
θ
≠
(
2
n
+
1
)
π
2
,
n
∈
Z
and
i
=
√
−
1
, then
A
α
is an odd multiple of
π
2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
α
is an even multiple of
π
2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
α
is an odd multiple of
π
4
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
α
is an even multiple of
π
4
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution
The correct option is
C
α
is an odd multiple of
π
4
tan
(
α
+
i
β
)
=
e
i
θ
⇒
tan
(
α
+
i
β
)
=
cos
θ
+
i
sin
θ
Taking complex conjugate, we get
tan
(
α
−
i
β
)
=
cos
θ
−
i
sin
θ
tan
2
α
=
tan
[
(
α
+
i
β
)
+
(
α
−
i
β
)
]
⇒
tan
2
α
=
tan
(
α
+
i
β
)
+
tan
(
α
−
i
β
)
1
−
tan
(
α
+
i
β
)
tan
(
α
−
i
β
)
⇒
1
tan
2
α
=
1
−
tan
(
α
+
i
β
)
tan
(
α
−
i
β
)
tan
(
α
+
i
β
)
+
tan
(
α
−
i
β
)
⇒
cot
2
α
=
1
−
(
cos
2
θ
+
sin
2
θ
)
2
cos
θ
⇒
cot
2
α
=
0
[
∵
θ
≠
(
2
n
+
1
)
π
2
]
⇒
2
α
=
(
2
m
+
1
)
π
2
,
m
∈
Z
⇒
α
=
(
2
m
+
1
)
π
4
,
m
∈
Z
Suggest Corrections
1
Similar questions
Q.
If
tan
(
α
+
i
β
)
=
e
i
θ
;
where
α
,
β
∈
R
,
θ
≠
(
2
n
+
1
)
π
2
,
n
∈
Z
and
i
=
√
−
1
, then
Q.
If
tan
α
−
tan
β
=
m
and
cot
α
−
cot
β
=
n
, then prove that
cot
(
α
−
β
)
=
1
m
−
1
n
Q.
Let
f
:
R
→
R
be an invertible and a differentiable function defined by
f
(
x
)
=
{
x
2
+
a
x
−
6
,
x
≤
2
α
x
2
+
β
,
x
>
2
where
a
,
β
∈
Z
,
α
∈
R
and
a
≥
−
5.
If
f
−
1
denotes the inverse function of
f
,
then
Q.
If
α
and
β
are real then
∣
∣
∣
α
+
i
β
β
+
i
α
∣
∣
∣
=
Q.
If
sin
(
α
+
β
)
=
1
and
sin
(
α
−
β
)
=
1
2
where
0
≤
α
,
β
≤
π
2
then find the value of
tan
(
α
+
2
β
)
tan
(
2
α
+
β
)
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
MATHEMATICS
Watch in App
Explore more
Euler's Representation
Standard XI 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