Prove arcsin x for its logarithm form

  • #1

Homework Statement


Given sin x = (eix - e-ix) / 2i,
I want to prove that

arcsin x = -i ln(ix + √1 - x2)

Homework Equations


I know about the Euler's formula and complex number. But I have never learnt about complex logarithms.

The Attempt at a Solution


I try to use x = sin y. But it seems not working. How to show that relation?
 

Answers and Replies

  • #2
13,169
7,065
Why not try working it backward? Take the arcsin x and substitute it into the first equation for x.
 

Related Threads on Prove arcsin x for its logarithm form

  • Last Post
Replies
5
Views
2K
  • Last Post
Replies
6
Views
2K
  • Last Post
Replies
7
Views
2K
  • Last Post
Replies
6
Views
3K
Replies
4
Views
2K
Replies
2
Views
4K
Replies
4
Views
1K
  • Last Post
Replies
2
Views
1K
Replies
16
Views
9K
  • Last Post
Replies
2
Views
6K
Top