Perform each operation. Write answers in standard form. (-8+2i)(-1+i)

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.

To multiply complex numbers, you apply the distributive property (also known as the FOIL method for binomials). This involves multiplying each part of the first complex number by each part of the second, and then combining like terms, remembering that i^2 = -1. This process is crucial for obtaining the product in standard form.

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