Complex Numbers

Operations with Complex Numbers

Complex numbers are numbers of the form a + bi, where a and b are real numbers and i is the imaginary unit, defined by . In Precalculus, understanding how to perform operations with complex numbers and express results in standard form is essential.

• Addition and Subtraction: To add or subtract complex numbers, combine the real parts and the imaginary parts separately.

• Multiplication: Use the distributive property (FOIL method) and apply to simplify.

• Standard Form: After performing operations, always write the result as a + bi.

Key Formulas

• Addition:

• Subtraction:

• Multiplication:

Example

• Addition Example:

• Multiplication Example:

Additional info: The standard form a + bi is used to clearly separate the real and imaginary components, which is important for further operations such as division and finding complex conjugates.