Need help to understand notation

Question

Can somebody explain the use of ange brackets in the book I'm reading now? On pages 1–2 of Krantz's Function theory of several complex variables (2nd ed., 1992), I see the following: if $dz_j=dx_j+i\,dy_j$ is a differential and $\frac{\partial}{\partial z_j}=\frac12\Bigl(\frac{\partial}{\partial x_j}+i\frac{\partial}{\partial y_j}\Bigr)$ is a partial differential operator, then $\Bigl\langle{dz_j,\frac{\partial}{\partial z_j}}\Bigr\rangle=1$. What is this operation called? An inner product of a differential form and a differential operator? What should I google for? Any explanatory books?