If `(x+i y)(p+i q)=(x^2+y^2)i` , prove that `x=q ,y=pdot`

x^(p)*y^(q) = (x+y)^(p+q) prove that dy/dx= y/x

If x^(p)y^(q)=(x+y)^(p+q) , prove that (dy)/(dx)=(y)/(x)

If x+iy=(1+2i)/(2+i) prove that x^(2)+y^(2)=1

If x^(p)y^(q)=(x+y)^(p+q) , show that dy/dx=y/x .

If x+iy=sqrt((1+i)/(1-i)), prove that x^(2)+y^(2)=1

If (log x)/(q-r)=(log y)/(r-p)=(log z)/(p-q) prove that x^(q+r)*y^(r+p)*z^(p+q)=x^(p)*y^(q).z^(r)

If x=1+i sqrt(3),y=1-i sqrt(3),z=2 then prove that x^(p)+y^(p)=z^(p) for every prime p>3

(i) If x+iy=(a+ib)/(a-ib) , prove that x^(2)+y^(2)=1 . (ii) If ((a+i)^(2))/(2a-i)=p+iq , prove that: p^(2)+q^(2)=((a^(2)+1)^(2))/(4a^(2)+1) .