1. If (x+iy)^1/3=a+ib, x,y,a,b E R.Show that x/a+y/b=4(a^2-b^2)

Dear Kurma,

after cubing given eqn we get

 x+iy=a^3-ib^3+3aib(a+ib)

       =a^3-ib^3+3a^2ib-3ab^2

      =a^3-3ab^2+i(3a^2b-b^3)    

comparing

x=a^3-3ab^2,y=3a^2b-b^3

x/a+y/b=a^2-3b^2+3a^2-b^2

          =4(a^2-b^2)

proved 

hope i helped u

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