Question

Let U⊆C∖0 be an open path-connected simply connected set, and fix z0∈U. Recall by lecture 18 that an anti-derivative for 1/z.

Answer 1

In complex analysis, an open, path-connected, simply connected set U⊆C∖0 is defined. The anti-derivative for 1/z is found to be log(z), where log is the complex logarithm function.

Step-by-step explanation:

In complex analysis, an open, path-connected, simply connected set U⊆C∖0 can be defined. Let's say we fix z0∈U. Now, we need to recall that an anti-derivative for 1/z can be found. The anti-derivative for 1/z is log(z), where log is the complex logarithm function. In other words, log(z) satisfies the property that its derivative is 1/z.