Complex Analysis 01: Inequalities

The two basic inequalities, and an application

[Mart-B]

Heads up for people: as he says in the intro, I wouldn't start with this playlist if you're new to Complex Analysis. It's an excellent playlist for moderate to advanced Complex students though.

For beginners, there's a playlist called Analysis of a Complex Kind, narrated by a German woman called Petra (at least I think she's German, my memory is failing me!), that was a lifesaver for me. She goes super slow yet in depth. It's a brilliant playlist.

Then I'd use this playlist after you've completed her playlist.

Oh and there's two really fast playlists that I wouldn't bother with - one was called Whirlwind Complex Analysis and the other one is called A Whirlwind Tour of Basic Complex Analysis. Both were very confusing and I wasted a lot of time on them.

The MIT one also looks good but it's quite short. That could be another good one for beginners. Good luck!

[tomatoboard]

Thank you. This series has allowed me to quickly understand some of the key theorems in my current complex analysis course.

[ssss]

That explanation for the second triangle inequality is really good. Thank you.

[KingGrio]

That illustration of the second triangle inequality with the distance between the two circles is really good and I agree it's a shame it's not in every textbook.

Thank you !

[jwyliecullick]

Elegant introduction to advanced topics. Thank you!

[bavanthaudugama]

yeah... this is really good lecture series... I have survived myself within one day by using this series.... but I think you may need basics to continue on this.... Lecturer clearly explains about residue theorem and all lectures focused on the way that student will be able to understand the whole picture about it.Also within few hours you could be able to be a expert on this part of complex you very much sir....

[kompik]

Isn't the "circle inequality" in this video usually called "reverse triangle inequality"? At least it is mentioned under this name on Wikipedia and Google returns also several other hits.

[GoogleUser-eero]

it is not complete play list is it? unless 2069 also has a calculus component like 1141 and 1241?

[edwinulat]

1. Suppose that z0 ∈ C is fixed. A polynomial P(z) is said to be divisible by z − z0 if there is another
polynomial Q(z) such that P(z) = (z − z0)Q(z).
a) Show that for every c ∈ C and k ∈ N, the polynomial c(z
k − z
k
0
) is divisible by z − z0.
b) Consider the polynomial P(z) = a0 + a1z + a2z
2 + . . . + anz
n, where a0, a1, a2, . . ., an ∈ C are
arbitrary. Show that the polynomial P(z) − P(z0) is divisible by z − z0.
c) Deduce that P(z) is divisible by z − z0 if P(z0) = 0.
d) Suppose that a polynomial P(z) of degree n vanishes at n distinct values z1, z2, . . ., zn ∈ C, so
that P(z1) = P(z2) = . . . = P(zn) = 0. Show that P(z) = c(z − z1)(z − z2). . .(z − zn), where
c ∈ C is a constant.
e) Suppose that a polynomial P(z) of degree n vanishes at more than n distinct values. Show that
P(z) = 0 identically.

[skylerpretto]

I actually find the "circle inequality" rather intuitive.

[LucianoRobino]

MATH 2069!? This is math from the FUTURE!!!!

[edwinulat]

compute all the values and plot them on the plane:
a) (1 + i)−1/2
b) (−4)3/4
c) (1 − i)3/8
kindly answer this pls

[savanzala]

sir is there any video for analytic complex
i desperately need it....

[ancient_hinduu]

sir, we are Indian and we like to solve maths problem day and night.plz extend your video time limit.