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    Hi guys.
    I know you're probably occupied with your AEA, but could you give me a lil push in the right direction.
    If Z=tanx+i 0<x<pi/2
    w=4(cospi/10+isinpi/10)
    how do i find the argument for z and Z/w? and |zw|?

    Thanks guys/girls.
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    (Original post by Goldenratio)
    Hi guys.
    I know you're probably occupied with your AEA, but could you give me a lil push in the right direction.
    If Z=tanx+i 0<x<pi/2
    w=4(cospi/10+isinpi/10)
    how do i find the argument for z and Z/w? and |zw|?

    Thanks guys/girls.
    argz=arctan(1/tanx)=arctan(cotx) [as tanx>0 in the given interval]
    tan(0.5pi-x)=cotx.
    argz=arctan[tan(0.5pi-x)]
    argz=0.5pi-x.

    arg(z/w)=argz-argw=(0.5pi-x)-(pi/10).
    arg(z/w)=2pi/5 - x

    |zw|=|z||w|=[(tanx)^2+1]^0.5[4]
    |zw|=4secx
    • Thread Starter
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    Thanks gaz!
    i still don't understand how/why the argument of z was pi/2-x though... sorry
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    Gaz showed that argz = arctan(cotx), then he used the identity cotx = tan(pi/2 - x) to get:
    argz = arctan(tan(pi/2 - x)) = pi/2 - x
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    Okay thank you.
    But why did you do pi/2-x in the first place instead of simply x, if it's in the first quadrant?
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    It's not about quadrants - we want to express argz in its simplest form.

    We have arctan(cotx). Recall that arctan(tanx)=x, which we could use by applying the identity: tan(pi/2 - x) = cotx
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    thank you
 
 
 
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