Find each sum or difference. Write answers in standard form. (3+2i) + (9+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, 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 and subtraction.

Addition of Complex Numbers

To add complex numbers, you combine their real parts and their imaginary parts separately. For example, when adding (3 + 2i) and (9 + 3i), you add 3 and 9 to get 12, and 2i and 3i to get 5i, resulting in the sum 12 + 5i. This process highlights the importance of treating real and imaginary components distinctly.

Standard Form of Complex Numbers

The standard form of a complex number is a + bi, where a and b are real numbers. Writing complex numbers in this form is crucial for clarity and consistency in mathematical communication. In the context of the question, the final answer should be expressed in this standard form after performing the addition.