SOLUTION: If x+iy=(a+ib)*(a+ib)*(a+ib) then show that x/a+y/b=4(a^2-b^2) PLZ help!!!!

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: If x+iy=(a+ib)*(a+ib)*(a+ib) then show that x/a+y/b=4(a^2-b^2) PLZ help!!!!      Log On


   

Question 319748: If x+iy=(a+ib)*(a+ib)*(a+ib) then show that x/a+y/b=4(a^2-b^2)
PLZ help!!!!
Answer by J2R2R(94) About Me  (Show Source):
You can put this solution on YOUR website!
x+iy = (a+ib)^3 = a^3 + 3a^2ib + 3ai^2b^2 + i^3b^3 = (a^3 - 3ab^2) + (3a^2b - b^3)i

Comparing real and imaginary components:
x = a^3 - 3ab^2; x/a = a^2 - 3b^2
y = 3a^2b - b^3; y/b = 3a^2 - b^2

x/a + y/b = 4(a^2 - b^2)