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

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, b is the imaginary part, and i is the imaginary unit defined as the square root of -1. Understanding complex numbers is essential for performing operations such as addition, subtraction, multiplication, and division.

Squaring a Binomial

Squaring a binomial involves applying the formula (a + b)² = a² + 2ab + b². This formula is crucial for expanding expressions like (2 + i)², where you identify a and b as 2 and i, respectively. Mastery of this concept allows for the correct expansion and simplification of polynomial expressions.

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, it is important to express the final result in this form for clarity and consistency. This involves combining like terms and ensuring that the imaginary unit is properly represented.