← Math: Complex Numbers

⇄ Sync
Length

Program
History and progress transfer
Choose a topic — problems will keep coming one after another for as long as you like

Theory of all steps of the program by blocks. Open a topic to read it.

How a session goes

A session is 10–90 minutes: a warm-up on what you've learned, new steps with short theory and problems, practice. Each problem gives two tries: 100 points on the first, 60 on the second; after the second mistake the correct answer is shown. You move on in the program if 70 % of the problems are solved.

Problems with numbers are generated anew every time a step is repeated. A fractional answer can be entered with a comma, a point or as a fraction: 0,5, 0.5, 1/2. In Practice any topic is available without a timer.

About the course

The imaginary unit and operations, the conjugate and division, quadratic equations with D < 0, the complex plane, modulus and argument, trigonometric form, multiplication as rotation, De Moivre's formula, n-th roots, and an overview of Euler's formula. Requires quadratic equations and trigonometry.

Course program: 25 lessons

The imaginary unit and operations

  1. The imaginary unit
  2. Algebraic form z = a + bi
  3. Addition and subtraction
  4. Multiplication
  5. Operations: more
  6. Checkpoint: the imaginary unit and operations

Conjugate, division, equations

  1. The conjugate
  2. Division
  3. Division: more
  4. Quadratic equations with D < 0
  5. Checkpoint: division and equations

The complex plane

  1. The complex plane
  2. Modulus
  3. Argument
  4. Modulus and argument: more
  5. Checkpoint: the complex plane

Trigonometric form

  1. Trigonometric form
  2. Multiplication as rotation and scaling
  3. De Moivre's formula
  4. Powers and rotations: more
  5. Checkpoint: trigonometric form

Roots and Euler's formula

  1. n-th roots
  2. Roots: more
  3. Euler's formula (overview)
  4. Checkpoint: roots and Euler's formula