We show how the generalized Cauchy integral formula motivates the Cauchy transform and gives that the Cauchy transform of the anti-conformal part of the gradient of a function is it function itself. We introduce the Log transform and show it commutes with translations and hence with derivatives, we show that the conformal part of the gradient of the log transform of a function is the Cauchy transform of the function. It will be needed to show that Cauchy transform is the inverse of taking the ant-conformal part of a gradient which will be shown in the next class.
