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

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

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

If z_(1) = 2 - i and z_(2) = -4 + 3i, find the inverse of z_(1)z_(2) and (z_(1))/(z_(2)) .

If z=1+i tan alpha where pi lt alpha lt(3pi)/(2), then what is |z| equal to ?

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