Intro Complex Analysis, Lec 9, Facts to Recall, Animations, Continuity Proofs (z^2 and 1/z)

Lecture 9. (0:00) Why is the empty set open (made a mistake in Lecture 8). (2:17) Typing up loose ends from chapter 1: the conjugate mapping reflects across the real axis, conjugation is operation preserving, the square of the modulus is the product of a complex number and its conjugate, facts about Re(z) and Im(z), nth roots. (9:28) Fun with mappings. (15:22) Prove that the limit as z approaches 3 + 4i of z^2 is -7 + 24i by doing some scratch work first (also need the Triangle Inequality). (40:21) Prove that the limit as z approaches 3 + 4i of 1/z is (3 - 4i)/25 (again do some scratch work first). (53:31) Open disks are open sets. (53:99) Linear approximations of differentiable complex functions have a special form.

AMAZON ASSOCIATE
As an Amazon Associate I earn from qualifying purchases.

[nicholaskhawlu]

Magnitude(3+4i+z-z)
25<1+magnitude(z)
Magnitude(z)>24
Magnitude(z)>1
1/magnitude(z)<1