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

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 = cos alpha + i sin alpha then the amplitude of z^2+barz is:

If z=(1+7i)/((2-i)^2) , then find |z|?

If z = ((1+i)^(2))/(alpha-i) , alpha in R has magnitude sqrt((2)/(5)) then the value of alpha is (i) 3 only (ii) -3 only (iii) 3 or -3 (iv) none of these

If omega = z//[z-(1//3)i] and |omega| = 1 , then find the locus of z.

If z= 1/((1+i)(1-2i)) , then |z| is

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

If the remainders respectively when f(z) = z^(3)+z^(2)+2z+1 is divided with z-i and z+i are 1+3i and 1+i then find the remainder when f(z) is divided with z^(2)+1 ?

If z=(3-sqrt(7)i) , then find |z^(-1)| .

If x + y + z = xyz and x, y, z gt 0 , then find the value of tan^(-1) x + tan^(-1) y + tan^(-1) z