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