∴
Complex Numbers
High School
Definition
A number combining real and imaginary parts, written as a + bi where i² = -1.
Formulas
z = a + bi
Standard form of complex number
- aReal part
- bImaginary part
- iImaginary unit (i² = -1)
|z| = √a² + b²
Absolute value (modulus)
\barz = a - bi
Complex conjugate
(a+bi)(c+di) = (ac-bd) + (ad+bc)i
Complex multiplication
Examples
Example 1
Calculate (3 + 2i) + (1 - 4i).
Example 2
Calculate (2 + 3i)(1 - 2i).
Applications
Electrical Engineering
AC circuit analysis
Physics
Quantum mechanics, waves
Computer Graphics
2D rotation, fractals
Related Documents
Was this page helpful?