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

  1. Mar 23, 2007 #1

    inv

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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: Mar 24, 2007
  2. jcsd
  3. Mar 23, 2007 #2

    mjsd

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    Homework Helper

    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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