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Class prep · TJ Complex Analysis

Keep the algebra exact,then read the plane.

An independent course in complex analysis. Compute with complex numbers, analytic functions, contour integrals, series and residues, and say what each result means on the plane. Every problem has a full worked solution. Built by Neil Kothari, a TJ alumnus.

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$395 covers the full school year. The first lesson is free.

Try one. This is a test-level question from the course.

Problem 1

  • Test level
  • Multiple choice
  • No calculator
  • 4 pts

Which number equals 1/(3+2i)1/(3+2i)?

Choose one answer

original problems, each with a worked answer
624
original problems, each with a worked answer
at test level or beyond
432
at test level or beyond
short lessons, one for every topic
48
short lessons, one for every topic
units, all open now
8
units, all open now

Free lesson

Lesson 1.1: Modulus, Conjugate and Rectangular Form

Compute with x+yi, and say what the modulus and conjugate mean on the plane.

Start with rectangular form, the conjugate and the modulus. Treat each number as a point, and finish every quotient with a real denominator.

Problem 2

  • Core
  • True or false
  • No calculator
  • 2 pts

True or False: ∣3+2i∣=5|3+2i| = 5. Justify.

Is the statement true or false?

Problem 3

  • Core
  • Multiple choice
  • No calculator
  • 4 pts

What is ∣3+2i∣2|3+2i|^2?

Choose one answer

Open the rest of this lesson, free

The full lesson and all 13 of its problems, with every worked answer.

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How it works

Class prep that works alongside class

A complete complex analysis course for students who have finished multivariable calculus. Work alongside your school course or study the material in sequence. Each lesson starts with a definition, develops one identity, and shows a check before you try the practice.

  • Original problems in several formats: true or false, multiple choice, multi-part and free response.
  • Each one is marked core, test level or beyond.
  • Rectangular and polar form, analytic functions, elementary functions, contour integrals, Cauchy's theorem, series, residues and conformal maps.
  • A worked answer for every problem, ending with the mistake that most often costs points.
  • The complex plane, differentiability, exponentials and logarithms, path integrals, Cauchy's formula, Laurent series, residues and simple mappings.

What is inside

  1. 1The complex plane6 lessons · 78 problems
  2. 2Analytic functions6 lessons · 78 problems
  3. 3Elementary functions6 lessons · 78 problems
  4. 4Contour integrals6 lessons · 78 problems
  5. 5Cauchy's theorem6 lessons · 78 problems
  6. 6Series6 lessons · 78 problems
  7. 7Residues6 lessons · 78 problems
  8. 8Conformal maps6 lessons · 78 problems
The front entrance of Thomas Jefferson High School for Science and Technology
Neil Kothari, co-founder of EduAvenues

Who built it

Neil Kothari

TJHSST alumnus · Co-founder, EduAvenues · 10+ years in TJ preparation

Neil is a TJ alumnus and has spent more than a decade working with TJ students and their families. He built this course so students can compute an exact complex value and then name the geometric reason it is right. Every problem is written for the course and every answer is checked before it goes in.

Tuition

$395for the full school year

One tuition covers every unit of the course. All 8 units are open now. The Modulus, Conjugate and Rectangular Form lesson stays free for everyone.

  • All 8 units: 48 lessons and 624 original problems
  • A worked answer for every problem
  • Access through the end of the school year
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