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

The inequality |z-i| lt |z + i| represents the region

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

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

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

If z is purely imaginary then and Im(z)gt0 , then amp(z)=

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 the following properties: Re(z) = (z + bar(z))/(2) and Im(z) = (z - bar(z))/(2i)

For any two complex numbers, z_1 and z_2 , prove that Re( z_1 z_2 ) = [(Re( z_1 ). Re( z_2 )] - [Im( z_1 ). Im( z_2 )]

If 0 lt amp(z) lt pi , then amp(z) - amp(-z) =