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 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) for which P^2=-I is

Let z=(-1+sqrt(3)i)/(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 ______.

Let z=(-1+sqrt(3)i)/(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 ______.

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(2-2sqrt(3i))^2=i(sqrt(3)+i)^4, then a r g(z)=

If |z-2-i|=|z|sin(pi/4-a r g z)| , where i=sqrt(-1) ,then locus of z, is

If |z-2-i|=|z|sin(pi/4-a r g z)| , where i=sqrt(-1) ,then locus of z, is

If z_(1)=3i and z_(2)=-1-i , where i=sqrt(-1) find the value of arg ((z_(1))/(z_(2)))

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