If `|z|=1` and `w=(z-1)/(z+1)` (where `z!=-1),` then `R e(w)` is 0 (b) `1/(|z+1|^2)` `|1/(z+1)|,1/(|z+1|^2)` (d) `(sqrt(2))/(|z|1""|^2)`

If |z|=1 and z'=(1+z^(2))/(z) , then

If z_(1)=3i and z_(2)=-1-i , where i=sqrt(-1) find the value of arg ((z_(1))/(z_(2)))

If |z-(1/z)|=1, then a. (|z|)_(m a x)=(1+sqrt(5))/2 b. (|z|)_(m in)=(sqrt(5)-1)/2 c. (|z|)_(m a x)=(sqrt(5)-2)/2 d. (|z|)_(m in)=(sqrt(5)-1)/(sqrt(2))

If |z|=1 and let omega=((1-z)^2)/(1-z^2) , then prove that the locus of omega is equivalent to |z-2|=|z+2|

. Ifx y+y z+z y=1,w h e r ex , y , z in R^+ , then x/(1+x^2)+y/(1+y^2)+z/(1+z^2)=2/(sqrt((1+x^2)(1+y^2)(1+z^2)))

If |z_(1)|=|z_(2)|=1 and argz_(1)+argz_(2)=0 then show that z_(1)=1

Let a be a complex number such that |a|<1a n dz_1, z_2,z_3,... be the vertices of a polygon such that z_k=1+a+a^2+...+a^(k-1) for all k=1,2,3, T h e nz_1, z_2 lie within the circle (a) |z-1/(1-a)|=1/(|a-1|) (b) |z+1/(a+1)|=1/(|a+1|) (c) |z-1/(1-a)|=|a-1| (d) |z+1/(a+1)|=|a+1|

If w=z/[z-1/(3i)] and |w|=1, then find the locus of z

If z_(1)=-3+4i and z_(2)=12-5i, "show that", |(z_(1))/(z_(2))|=(|z_(1)|)/(|z_(2)|)

If |z_1/z_2|=1 and arg (z_1z_2)=0 , then a. z_1 = z_2 b. |z_2|^2 = z_1*z_2 c. z_1*z_2 = 1 d. none of these