Question

If ³√a+ib = x + iy then use this to prove
a/x + b/y = 4 ( x² - y²) ​

Answer 1

Answer:

Given, (x+iy)3=u+iv

x3+(iy)3+3.x.iy(x+iy)=u+iv

x3+i3y3+3x2yi+3xy2i2=u+iv

x3−iy3+3x2yi−3xy2=u+iv

(x3−3xy2)=i(3x2y−y3)=u+iv

On equating real and imaginary parts, we get

u=x3−3xy2,v=3x2y−y3

∴xu+yv=xx3−3xy2+y3x2y−y3

=