The book uses the notation of a complex flow $F(z)=u-iv$, with a function $W=\phi + i\psi$ such that $F=\frac{dW}{dz}$.
The book gives the following example:
Choose $$W(z) =\frac{\Gamma}{2\pi i}\log(z-z_0)$$ where $\Gamma$ and $z_0$ are some constants. Then [...] $\psi$ is constant on any circle centered at $z_0$.
Shouldn't it be $\phi$ that's constant? The real part of $W$ is $\phi=\frac{\Gamma}{2\pi i}\log(|z-z_0|)$, which is constant on circles centred at $z_0$. The imaginary part, $\psi$ is a function of $\arg(z)$, which is certainly not constant on any circle.
The book also has the following diagram:
What am I missing here?
