Products and Quotients of Complex Numbers

Multiplying and Dividing 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 . Operations such as multiplication and division can be performed using algebraic rules and properties of i.

Multiplication of Complex Numbers

• Definition: To multiply two complex numbers, use the distributive property (FOIL method) and simplify using .

• Formula:

• Example: (since )

Division of Complex Numbers

• Definition: To divide complex numbers, multiply numerator and denominator by the conjugate of the denominator.

• Formula:

• Conjugate: The conjugate of is .

• Example: Multiply numerator and denominator by : Numerator: Denominator:

Practice Problems

Additional info: Mastery of these operations is essential for solving equations involving complex numbers and for applications in trigonometry, engineering, and physics.