Find each product. Write answers in standard form. (√6+i)(√6-i)

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.

Conjugates

The conjugate of a complex number a + bi is a - bi. When multiplying a complex number by its conjugate, the result is a real number, specifically a² + b². This property is useful for simplifying expressions and finding products, as it eliminates the imaginary part.

Standard Form of Complex Numbers

The standard form of a complex number is expressed as a + bi, where 'a' and 'b' are real numbers. When performing operations with complex numbers, such as multiplication, the result should be simplified to this form for clarity and consistency, making it easier to interpret the real and imaginary components.