This is a collection of practice problems and solutions on the topic of complex numbers from around the web. (Currently, all problems concern arithmetic and algebra with complex numbers.) A few of the problems were written by our tutors but most of the material was created by instructors at various universities and colleges for their introductory math courses. The content here takes the form of worksheets, homework, quizzes, and tests, with solutions provided in all cases. We’ve also included some of the best relevant references and videos available online.

We think these questions, solutions, and references make for excellent material for students learning about complex numbers (in high school or college) or those engaged in self study. Please write to us at info@wordpress-526411-2682118.cloudwaysapps.com/library if you have any questions or suggestions. Happy learning!

#### Cartesian and polar representation, arithmetic operations (including nth roots) and exponentials (Euler's identity)

**Worksheet and solutions (CERN summer school) || ** **Exercises (Prof Swenson, UC Berkeley);** **Solutions ****||** **Worksheet 1,** **Solutions**; **Worksheet 2, ****Solutions**; **Worksheet 3,** **Solutions** (Profs Mattuk and Miller, MIT) **||** **Tutor Terrace Worksheet and Solutions || Homework (Prof Calegari, Harvard); Solutions || ****Practice test (Prof McKernan, UCSD);** **Solutions || Worksheet, Solutions **(Dr. Lavrov, Carnegie Mellon University)

**A note on complex arithmetic by Dr. Jorloff (MIT)**.

**Another note on complex numbers by Prof Zager (MIT)**.

**An hour on complex numbers Harvard University (Oliver Knill) **is an excellent overview of complex number topics.

**Chapter 2.4 of this textbook from OpenStax** has a clear discussion of complex numbers and their arithmetic.

**This excellent video from 3Blue1Brown **discusses the fundamentals of complex numbers.

**This lecture by Prof Strang of MIT** is a great introduction to complex numbers.

**This video by Prof Gralla (Tutor Terrace)** discusses the roots of complex numbers.