If `k + |k + z^2|=|z|^2(k in R^-)`, then possible argument of z is

If z is a complex number satisfying z^4+z^3+2z^2+z+1=0 then the set of possible values of z is

If |z|=1 and z ne +-1 , then one of the possible value of arg(z)-arg(z+1)-arg(z-1) , is

If the system of equations x-k y-z=0, k x-y-z=0,x+y-z=0 has a nonzero solution, then the possible value of k are -1,2 b. 1,2 c. 0,1 d. -1,1

If a rg(z_1)=170^0a n d arg(z_2)=70^0 , then find the principal argument of z_1z_2dot

If z is a complex number lying in the fourth quadrant of Argand plane and |[(kz)/(k+1)]+2i|>sqrt(2) for all real value of k(k!=-1), then range of "a r g"(z) is a. (pi/8,0) b. (pi/6,0) c. (pi/4,0) d. none of these

Let z be not a real number such that (1+z+z^2)//(1-z+z^2) in R , then prove tha |z|=1.

If w(x,y,z) = x^2y+y^2z + z^2x,x,y,z in R, find the differential dw.

If the line (x-2)/-1=(y+2)/1=(z+k)/4 is one of the angle bisector of the lines x/1=y/-2=z/3 and x/-2=y/3=z/1 then the value of k is