separate real and imaginary part of tan inverse (alpha+i
beta)
Answers
Answered by
0
Answer:
university
Step-by-step explanation:
I hope you understand m
Answered by
0
Answer:
Hope will hell you the answer
Step-by-step explanation:
Let α+iβ=tan
−1
(x+iy)
Then α−iβ=tan
−1
(x−iy)
Adding, we get
2α=tan
−1
(x+iy)+tan
−1
(x−iy)
⇒tan
−1
(
1−(x+iy)(x−iy)
x+iy+x−iy
)
∴ Real part α=
2
1
tan
−1
(
1−(x+iy)(x−iy)
x+iy+x−iy
)
Subtracting, 2iβ=tan
−1
(x+iy)−tan
−1
(x−iy)
⇒2iβ=tan
−1
(
1+(x+iy)(x−iy)
(x+iy)−(x−iy)
)
⇒2iβ=tan
−1
(
1+x
2
+y
2
2iy
)
⇒2iβ=itanh
−1
(
1+x
2
+y
2
2y
)
∴ Imaginary part β=
2
1
tanh
−1
(
1+x
2
+y
2
2y
)
Similar questions