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# complex numbers w trig watch

1. 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.
2. (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
3. Thanks gaz!
i still don't understand how/why the argument of z was pi/2-x though... sorry
4. 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
5. 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?
6. 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
7. thank you

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