• Support PF! Buy your school textbooks, materials and every day products Here!

U=2+i.By considering the arg of u/u* or otherwise how prove tan^-1(4/3)=2tan^-1(0.5)?

  • Thread starter inv
  • Start date
  • #1
inv
46
0
[Solved]u=2+i.By considering the arg of u/u* or otherwise

*Solved


Homework Statement


u=2+i.
u*=2-i
"By considering the arg of u"/u* or otherwise prove that tan^-1(4/3)=2tan^-1(0.5).That's the question,explain how do pls?

Homework Equations


arg(u/u*)=arg u -arg u*
tan A=opposite side/adjacent side
tan2A=2tanA/(1-tan^2 A)

The Attempt at a Solution


tanA=1/2
2tanA=1
tan2A(1-tan^2 A)=1
*Stuck here,guide pls?

Edit*
 
Last edited:

Answers and Replies

  • #2
mjsd
Homework Helper
726
3
draw you complex numbers on an argand diagram
observe that arg u and arg u* are the same... arg u + arg u* = arg u - (-arg u) = 2 arg u
and that tan^-1 x gives you an angle.
 

Related Threads on U=2+i.By considering the arg of u/u* or otherwise how prove tan^-1(4/3)=2tan^-1(0.5)?

Replies
3
Views
3K
Replies
6
Views
1K
  • Last Post
Replies
2
Views
800
  • Last Post
Replies
11
Views
6K
  • Last Post
Replies
2
Views
4K
  • Last Post
Replies
6
Views
2K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
20
Views
1K
  • Last Post
Replies
12
Views
4K
Replies
10
Views
1K
Top