We present a novel approach for bounding the resolvent of $$H=-\Delta +i(A·\nabla +\nabla ·A)+V=:-\Delta +L1$$ for large energies. It is shown here that there exist a large integer $m$ and a large number ${\lambda }_0$ so that relative to the usual weighted $L^2$-norm, $$\parallel {\left(L{(-\Delta +(\lambda +i0))}^{-1}\right)}^m\parallel <\frac{1}{2}2$$ for all $\lambda >{\lambda }_0$. This requires suitable decay and smoothness conditions on $A,V$. The estimate (2) is trivial when $A=0$, but difficult for large $A$ since the gradient term exactly cancels the natural decay of the free resolvent. To obtain (2), we introduce a conical decomposition of the resolvent and then sum over...