Rotate and Fan Out Your Hand to Unlock the Geometry of Complex Analysis

Embodiment, specifically gesture, in conjunction with metaphors can unveil one’s reasoning about mathematics. In this talk, I will share what my colleagues and I have learned regarding visualization of complex analysis concepts. A pivotal finding is that understanding the geometry behind complex multiplication can unlock the geometry behind other inscriptions such as $$ f'(z)=dw/dz , ∫_C f(z)dz $$ and the Cauchy-Riemann equations. In concluding remarks, I will offer implications for teaching complex analysis and the role of embodiment.