Fermi · Concept Library · Courses · Books · Problems · Simulations · Math Wiki · High School Fermi › Problems A First Course in Complex Analysis · Problem 2.5.6
Differentiation — Beck, Marchesi, Pixton & Sabalka
Mathematics — Complex Analysis · limits-complex-functions
Problem Compute the following limits or explain why they don't exist.
((a)) lim z → 1 + i z 2 − 2 i z − 1 − i \displaystyle\lim_{z \to 1+i} \frac{z^2 - 2i}{z - 1 - i} z → 1 + i lim z − 1 − i z 2 − 2 i lim z → 0 Re ( z ) z \displaystyle\lim_{z \to 0} \frac{\operatorname{Re}(z)}{z} z → 0 lim z Re ( z ) lim z → 0 z 2 ∣ z ∣ 2 \displaystyle\lim_{z \to 0} \frac{z^2}{|z|^2} z → 0 lim ∣ z ∣ 2 z 2 lim z → i z 2 + 1 z 4 − 1 \displaystyle\lim_{z \to i} \frac{z^2 + 1}{z^4 - 1} z → i lim z 4 − 1 z 2 + 1 Browse the problem library