Find each product. Write answers in standard form. (-2-3i)(-2+3i)

Key Concepts

Complex Numbers

Complex numbers are numbers that have a real part and an imaginary part, expressed in the form a + bi, where 'a' is the real part and 'b' is the coefficient of the imaginary unit 'i', which is defined as the square root of -1. Understanding complex numbers is essential for performing operations such as addition, subtraction, multiplication, and division.

Multiplication of Complex Numbers

To multiply complex numbers, you apply the distributive property (also known as the FOIL method for binomials). For example, when multiplying (a + bi)(c + di), you multiply each part: ac, adi, bci, and bdi^2. Remember that i^2 equals -1, which is crucial for simplifying the result into standard form.

Standard Form of Complex Numbers

The standard form of a complex number is expressed as a + bi, where 'a' is the real part and 'b' is the imaginary part. When performing operations with complex numbers, the final answer should be simplified to this form, ensuring clarity and consistency in representation. This is important for further mathematical operations and interpretations.