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

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[Solved]u=2+i.By considering the arg of u/u* or otherwise

*Solved


1. The problem statement, all variables and given/known data
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?

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

3. The attempt at a solution
tanA=1/2
2tanA=1
tan2A(1-tan^2 A)=1
*Stuck here,guide pls?

Edit*
 
Last edited:

mjsd

Homework Helper
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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.
 

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