For a complex constant w prove Rew w w 2 Imw w w 2iSolu

For a complex constant “w”, prove: Re(w) = (w + w* )/2 ; Im(w) = (w – w* )/(2i).

Solution

Ans)

Let w=x+iy then w*=x-iy

(w+w*)/2=(x+iy+x-iy)/2=2x/2=x=Re(w) proves first equation

(w-w*)/2i=(x+iy-x+iy)/2i=i2y/2i=y=Im(w) proves second equation