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/z_2|=1 and arg (z_1z_2)=0 , then

If omega=(z)/(z-(1/3)i)" and "|omega|=1 , then z lies on

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|

If z^(2)+z+1=0 , where z is a complex number, then the value of (z+(1)/(z))^(2)+(z^(2)+(1)/(z^2))^(2)+(z^(3)+(1)/(z^3))^(2)+"……"+(z^(6)+(1)/(z^6))^(2) is

If |z_(1)+ z_(2)|=|z_(1)|+|z_(2)| , then arg z_(1) - arg z_(2) is

If |z-(1/z)|=1, then (|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))

Lt a be a complex number such that |a|<1a n dz_1, z_2z_, 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 z_(1) and z_(2) are 1 - i, -2 + 4i then find Im ((z_(1) z_(2))/(bar(z_(1)))) .

Let z_(1)=2-i, z_(2)= -2+i . Find (i) Re((z_(1)z_(2))/(z_1)) (ii) Im((1)/(z_(1)z_(2))) .