If `|u|=|v|=1` `uv!=-1` and `z=(u-v)/(1+uv)` then (a) `|z|=1` (b) `Re(z)=0` (c) `Im(z)=0` (d) `Re(z)=Im(z)`

|z-4| (a) Re(z) > 0 (b) Re(z) (c) Re(z) > 3 (d) None of these

If z!=0 be a complex number and arg(z)=(pi)/(4), then Re(z)=Im(z) only Re(z)=Im(z)>0Re(z^(2))=Im(z^(2))(d) None of these

If z=((sqrt3)/(2)+(1)/(2)i)^5+((sqrt3)/(2)-(i)/(2))^5 , then (a) im(z)=0 (b) Re(z)gt0 , Im(z)gt0 (c) Re(z)gt0 , Im(z)lt0 (d) Re(z)=3

|z-i|lt|z+i| represents the region (A) Re(z)gt0 (B) Re(z)lt0 (C) Im(z)gt0 (D) Im(z)lt0

|z-i|lt|z+i| represents the region (A) Re(z)gt0 (B) Re(z)lt0 (C) Im(z)gt0 (D) Im(z)lt0

Prove Im (z_ (1) z_ (2)) = Rez_ (1) .Im z_ (2) + Rez_ (2) .Im z_ (1)

Im ((1) / (z_ (1) bar (z) _ (1)))

If z=((sqrt(3))/(2)+(1)/(2)i)^(5)+((sqrt(3))/(2)-(i)/(2))^(5), then (a) im(z)=0 (b) Re(z)>0,Im(z)>0(c)Re(z)>0,Im(z)<0 (d) Re(z)=3

Prove that Re (z_ (1) z_ (2)) = Re z_ (1) Rez_ (2) -Im z_ (1) Im z_ (2)

For any two complex numbers z_(1)" and "z_(2) prove that (i) Re(z_(1)z_(2))=Re(z_1) Re(z_2)-Im(z_1)Im(z_2) .