[(A)Re(tau)>0quad (B)Re(T)<0],[[r(1+i)(1+2i)(1+3i)...(1+n(1)=a+i beta)then2*5+10...(1+n^(2))=],[(A)alpha-i betaquad (B)alpha^(2)-beta^(2)quad (C)(1)+P^(2)]

|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

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

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

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

In case of a radioactive element which of the following relations are not correct where, lambda = decay constant, T = half life and tau = mean life? (A) tau=1/lambda (B) tau=0.693/lambda (C) tau=0.6 T (D) tau =T/0.693

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)

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

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) .

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