let `z= (-1+sqrt(3i))/2, where i=sqrt(-1) and r,s epsilon P1,2,3}. Let P= [((-z)^r, z^(2s)),(z^(2s), z^r)]` and I be the idenfity matrix or order 2. Then the total number of ordered pairs (r,s) or which `P^2=-I` is

Let z = (-1 + sqrt(3i))/(2) , where i= sqrt(-1) , and r,s in {1,2,3} . Let P =:[((-z)^(r) ,z^(2s)),(z^(2s), z^(r))] and I be the identity matrix of order 2 .Then the total number of ordered pairs (r,s) for which p^(2) = - I is ______

If z=(-2(1+2i))/(3+i) where i=sqrt(-1) then argument theta(-pilt thetalepi) of z is

If |z-2i|lesqrt(2), where i=sqrt(-1), then the maximum value of |3-i(z-1)|, is

If |z-2-3i|+|z+2-6i|=4 where i=sqrt(-1) then find the locus of P(z)

let z_1,z_2,z_3 and z_4 be the roots of the equation z^4 + z^3 +2=0 , then the value of prod_(r=1)^(4) (2z_r+1) is equal to :

If z satisfies |z-1|<|z+3| then omega=2z+3-i, (where i=sqrt(-1) ) sqtisfies

Let z=((1+i)^(2))/(a-i),(a>0) and |z|=sqrt((2)/(5)) then z is equal to