In Exercises 48–57, perform the indicated operations and write the result in standard form. √ (-32) - √ (-18)

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 square roots of negative numbers, as they allow us to express these roots in a meaningful way.

The square root of a negative number is not defined within the set of real numbers, but it can be expressed using imaginary numbers. For example, √(-n) can be rewritten as i√n, where 'i' is the imaginary unit. This concept is crucial for solving problems that involve square roots of negative values, as seen in the given expression.

The standard form of a complex number is typically written as a + bi, where 'a' and 'b' are real numbers. When performing operations with complex numbers, such as addition or subtraction, it is important to combine like terms (real with real and imaginary with imaginary) to express the result in this standard form. This ensures clarity and consistency in mathematical communication.