Perform each operation. Write answers in standard form. (6-i) + (7-2i)

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 involving them, such as addition, subtraction, multiplication, and division.

Addition of Complex Numbers

To add complex numbers, you combine their real parts and their imaginary parts separately. For example, when adding (6 - i) and (7 - 2i), you would add 6 and 7 to get 13, and -1 and -2 to get -3i, resulting in the sum 13 - 3i. This process highlights the importance of treating the real and imaginary components distinctly.

Standard Form of Complex Numbers

The standard form of a complex number is expressed as a + bi, where 'a' and 'b' are real numbers. This format is crucial for clarity and consistency in mathematical communication. When performing operations on complex numbers, the final result should also be presented in this standard form to ensure it is easily interpretable.