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Deside the argument

  1. Apr 14, 2014 #1
    Hi im kind of lost
    Deside an argument for w


    w= (-4(√3+i))/(-1+i)

    I know that the arg is the angel..
    And the equation is in radians..

    where to start??

    best Regards!!




    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Apr 14, 2014 #2

    jbunniii

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    Convert to polar coordinates?
     
  4. Apr 14, 2014 #3
    yeah i thought so to, but im not really sure how..
    z=r cos σ+i r sinσ=r(cos+i sin), i dont know how to use this ...
     
  5. Apr 14, 2014 #4

    jbunniii

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    Hint: you should be able to convert these to polar coordinates easily:

    $$\frac{\sqrt{3}}{2} + i \frac{1}{2}$$
    and
    $$-\frac{1}{\sqrt{2}} + i \frac{1}{\sqrt{2}}$$
     
  6. Apr 14, 2014 #5

    Zondrina

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    Hint: Why don't you try multiplying the entire expression by: ##\frac{- 1 - i}{- 1 - i}##.

    Then switch to polar.
     
  7. Apr 14, 2014 #6
    i did try to multiply it, it gave me (3-√3+3i-√3i)/2 it looks wrong and it wont help me..
    sorry Jbunniii i can´t .. thanx for your time..
     
  8. Apr 14, 2014 #7
    With little help from my friend i manage solve it, thanks guys..
     
  9. Apr 14, 2014 #8

    jbunniii

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    Glad you were able to solve it. FYI, it's useful to remember the cosine and sine of three key angles: ##\pi/6##, ##\pi/4##, and ##\pi/3## (i.e., 30, 45, and 60 degrees). Then you can instantly recognize things like
    $$\frac{\sqrt{3}}{2} + i \frac{1}{2} = \cos(\pi/6) + i \sin(\pi/6)$$
     
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