Let `z_1=a+i b` and `z_2=c+i d` are two complex number such that `|z_1|=|z_2|=r` and `R e(z_1z_2)=0` . If `w_1=a+i c` and `w_2=b+i d ,` then (a)`|w_1|=r` (b) `|w_2|=r` (c)`R e(w_1w_2)=0` (d) `I m(w_1w_2)=0`

Let z_(1)=a+ib and z_(2)=c+id are two complex number such that |z_(1)|=|z_(2)|=r and Re(z_(1)z_(2))=0 .If w_(1)=a+ic and w_(2)=b+id, then (a) |w_(1)|=r( b) |w_(2)|=r (c) Re(w_(1)w_(2))=0 (d) Im(w_(1)w_(2))=0

Let z and w be two complex numbers such that |Z|<=1,|w|<=1 and |z+iw|=|z-ibar(w)|=2

Let Z and w be two complex number such that |zw|=1 and arg(z)-arg(w)=pi/2 then

If z_(1)=ai+bj and z_(2)=ci+dj are two vectors in i and j system,where |z_(1)|=|z_(2)|=r and z_(1).z_(2)=0 then w_(1)=ai+cj and w_(2)=bi+dj satisfy

If z and w are two complex number such that |zw|=1 and arg(z)arg(w)=(pi)/(2), then show that bar(z)w=-i

Let z and w be two non-zero complex number such that |z|=|w| and arg (z)+arg(w)=pi then z equals.w(b)-w (c) w(d)-w

Read the following writeup carefully: If z_1 = a+ib and z_2 =c + id be two complex numbers such that |z_1| = |z_2|=1 and "Re" (z_1 bar(z_2))=0 . Now answer the following question Let W = a+ic , then the locus of |(W+1)/(W-1)|=1 is (where W ne 1 )