Finding the Locus of a Complex Number with Given Conditions

[some1]

can some 1 help me tho solve this
a complex number, z satisfied the equation |z|=2
draw the locus W which satisfied the equation w=(z+2)/(z-1)
thx

 

[tiny-tim]

Welcome to PF!

Hi some1! Welcome to PF!

Hint: put z = re^iθ, and then use a complex conjugate to get rid of the complex denominator.

 

[some1]

still not really understand...can show the step??
thx

 

[gabbagabbahey]

still not really understand...can show the step??
thx

No, that's not what we do here. When you signed up for your account, you were instructed to read a set of guidelines. In those guidelines, it is made clear that we do not do your homework for you, you must make an effort and show your attempts. TinyTim gave you a good hint, how far do you get when you try to apply his hint? (Post what you've got!)

 

[tiny-tim]

Yes, you must show us your attempt …

if w=(z+2)/(z-1), and z = re^iθ, then what is w in terms of r and θ ?