If `z=(1+I tan alpha)^(1+i)`, then find the magnitude of Z.

If z=(1-i)^(6)+(1-i) , then find the modulus of z (i.e., |z|) and multiplicative inverse of z (i.e., z^(-1) ).

If z_(1)=2-i, z_(2)=1+ 2i, then find the value of the following : (i) Re((z_(1)*z_(2))/(bar(z)_(2))) (ii) Im (z_(1)*bar(z)_(2))

If z=3+4i, then find |z| and z^(-1) .

If Z+alpha|Z-1|+2i=0 , then find the sum of maximum and minimum values of alpha .( alpha in R )

If z = (1-i) , find z^(-1) .

If complex number z lies on the curve |z-(-1+i)|=1, then find the locus of the complex number w=(z+i)/(1-i),i=sqrt(-1)1

If w=(z)/(z-((1)/(3))i) and |w|=1, then find the locus of z and |w|=1, then find the

If z_1 = 3i and z_2 = -1 -i , find the value of arg z_1/z_2 .