If `(x+iy)^(5)=p+iq`, then prove that `(y+ix)^(5)=q+ip`

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

If (a+i)^2/(2a-i) = p+iq , prove that p^2+q^2 = (a^2+1)^2/(4a^2+1)

If x-iy=sqrt((a-ib)/(c-id) , prove that (x^2+y^2)^2 = (a^2+b^2)/(c^2+d^2)

If (x+iy)^3 = u + iv , then show that u/x+v/y=4(x^2-y^2)

If y=5 cos x-3 sin x , prove that (d^2y)/(dx^2)+y=0

If ^9p_5+5^9p_4=^10p_r .prove that r=5

If z = x+iy, prove that arg(z -1) = tan^(-1)(y/(x-1)) and arg(z+1) = tan^(-1)(y/(x+1))

If z=x-iy and z^(1/3)=p+iq , then (1)/(p^(2)+q^(2))((x)/(p)+(y)/(q)) is equal to

Find the real numbers x and y if (x-iy)(3+5i) is the conjugate of - 6 - 24i

If the 4^(th),10^(th) and 16^(th) terms of a G.P. are x,y and z respectively ,then prove that x,y,z are in G.P.P.