If `x=1 + i sqrt3, y= 1- i sqrt3 and z=2`, then prove that `x^(p)+ y^(p) + z^(p)` for every prime `p gt 3`.

If z (2- 2 sqrt3i)^(2)= i(sqrt3+i)^(4) , then arg(z)=

Let z _(1) = 1 + i sqrt3 and z _(2) = 1 + i, then arg ((z _(1))/( z _(2))) is

If z _(1) = 2 sqrt2 (1 + i) and z _(2) = 1 + isqrt3, then z _(1) ^(2) z _(2) ^(3) is equal to

If z=sqrt3+i , then the argument of z^2 e^(z-i) is equal to

If x,y, and z are in A.P ax , by and cz are in G.P. and a,b,c are in HP then prove that (x)/(z) +(z)/(x) = (a)/ (c )+(c )/(a)

If z=sqrt3+i , find the conjugate of Z.

If 2+ i sqrt3 is a root of the equation x^(2)+px+q=0 , where p and q are real then find the value of p and q.

If x,y,z are in G.P. and a^(x)=b^(y) =c^(z) then

If the mth, nth and pth terms of an A.P. and G.P.be equal and be respectively x, y, z then prove that x^(y-z) y^(z-x) z^(x-y)=1