Complex number

The set of complex numbers is denoted by . The complement of this set is , the real numbers. All complex numbers can be divided into two parts, the real part, denoted by or simply , and the imaginary part, denoted by or simply .

The letters and are usually used to denote complex numbers.

Operations

• Addition
• Subtraction
• Multiplication
• Division
• Absolute value/Modulus/Magnitude (denoted by ). This is the distance from the origin to the complex number when graphed.

Simple Example

If and ,

• ,
• 
• ,
• 
• 
• 

Topics

• Complex plane
• DeMoivre's Theorem
• Exponential form
• Roots of unity
• Geometry with complex numbers

See also

• Trigonometry
• Real numbers