Complex Analysis: Lecture 3: branch cuts, complex exponential

we begin by looking at the sixth root of unity. I mention the utility of this towards solving complex equations and factoring polynomials. I attempt, but fail, to present the solution of the quadratic equation (will add fix later). Then we turn our attention to the problem of finding local inverse functions in the complex domain. To make more sense of what I write for the nth root, solve z^n = w for z ( I did not do this) then you can either use Arg or Arg_alpha generally and this corresponds to various restrictions of the domain. Or, from the multiply-valued viewpoint, the selection of a branch. Then we define the complex exponential and derive the local inverse based on Arg which is denoted Log. The set of all possible solutions to exp(z)=w is denoted log(w). Next class we study the complex power function and the complex trigonometric and hyperbolic functions.

[georgesadler]

Professor Cook, thank you for an awesome lecture on branch cuts and complex exponential. These topics are important in Complex Analysis.

[aaronmarvel]

I dont understand the hate towards the prayer in the beginning. Im not religious myself, however, since it is a Christian university and they are teaching the right stuff with the right Prof, I dont see the problem lol Everyone's acting like the prayer in the beginning suddenly changed all the formulas into gibberish.

[ravikmoreiradarocha]

Great class (letting apart the first minute)

[fernandojackson]

Isn't the "Tiling" half-open (or half-closed ; depending on your mood ; ))?, i.e., of the type [a, a+ 2\pi), and not open? If you use, e.g., (0, i2\pi), instead of [0, i2\pi), the image will not include the Positive Real axis.

[beattoedtli]

Mistake at 32:25 it should be from -pi/n to pi/n

[kilogods]

yea dude a prayer before class.. that was freaking weird.