complex numbers

Basic idea

Extension of the reals by adjoining $i$ with $i^2=-1$. Algebraically closed: every non-constant polynomial has a root.

Key formulas

• $i^2=-1$
• Euler’s formula: $e^{i\theta}=\cos\theta+i\sin\theta$
• Modulus: $|a+bi|=\sqrt{a^2+b^2}$
• Conjugate: $\overline{a+bi}=a-bi$

Pages

• Complex Numbers

Siblings

• Blogs
• calculus
• linear algebra
• set theory