Find each sum or difference. Write answers in standard form. (-4-i) - (2+3i) + (-4+5i)

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 imaginary part. In this context, i represents the imaginary unit, defined as the square root of -1. Understanding how to manipulate complex numbers is essential for solving problems involving addition and subtraction of these numbers.

Standard Form of Complex Numbers

The standard form of a complex number is 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 standard form. This involves combining like terms, specifically the real parts and the imaginary parts separately, to ensure clarity and consistency in representation.

Addition and Subtraction of Complex Numbers

To add or subtract complex numbers, you combine their real parts and their imaginary parts separately. For example, when subtracting (2 + 3i) from (-4 - i), you subtract the real parts (-4 - 2) and the imaginary parts (-1 - 3). Mastery of this process is crucial for accurately solving problems that involve multiple complex numbers.