Post by mondo on Aug 12, 2022 5:33:28 GMT
On page 515, in the 3rd paragraph we have $\Phi(z) = \frac{S}{4}|z|^2$ and author says it generates $V = \frac{S}{2}z$. I believe the calculations he did were $\frac{d}{dx}(\frac{S}{4}(x^2 + y^2)) + \frac{d}{dy}(\frac{S}{4}(x^2 + y^2))$ hence we have $\frac{S}{4}(2x) + \frac{S}{4}(2y) = \frac{S}{2}(x+y))$
So it appears author replaced $(x+y)$ with $z$ but is it "legal" here? After all $(x+y) \neq $(x+iy) = z$. Another doubt comes from the fact that we were differentiating a real number $|z|^2$, a length of our complex vector $z$ squared and we got a complex number back? That doesn't sound right.
Thank you.
So it appears author replaced $(x+y)$ with $z$ but is it "legal" here? After all $(x+y) \neq $(x+iy) = z$. Another doubt comes from the fact that we were differentiating a real number $|z|^2$, a length of our complex vector $z$ squared and we got a complex number back? That doesn't sound right.
Thank you.
