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Complex numbers are an extension of the real number system. They include all real numbers and all imaginary numbers. A complex number has the form \(a + bi\), where \(a\) is the real part and \(bi\) is the imaginary part. Here, \(b\) is a real number, and \(i\) is the imaginary unit defined by the property \(i^2 = -1\).

Complex numbers allow us to perform calculations that involve square roots of negative numbers. For example, the square root of \(-1\) is not defined in the real number system but is represented by \(i\) in the complex system. This makes it possible to express any negative radicand in terms of complex numbers.

Understanding complex numbers is essential for working with problems involving imaginary numbers. They help solve equations that would otherwise have no real solutions, making them critical in various mathematical and engineering contexts.

Writing a number in its simplest form means expressing it in the most reduced state possible. For complex numbers, this often means eliminating negative radicands or other non-standard forms.

Consider the expression \(-\sqrt{-95}\). To simplify it, we decompose the negative sign under the square root using the imaginary unit \(i\). This results in \(\sqrt{-1} \times \sqrt{95}\), which simplifies to \(i\sqrt{95}\). Since there is a negative sign in front of the square root in the original expression, the simplest form becomes \(-i\sqrt{95}\).

Unlike real numbers, simple forms in complex numbers often include imaginary components. The goal is to clearly express them without radical or algebraic complexities. This approach also ensures that expressions are easier to understand and manipulate.

A negative radicand is a number with a negative sign inside the square root symbol. Normally in the real number system, the square root of a negative number is undefined. However, in complex numbers, this is handled using the imaginary unit \(i\).

For example, \(\sqrt{-95}\) has a negative radicand. By extracting \(\sqrt{-1}\) as \(i\), we convert the expression into an acceptable form for calculation and understanding: \(i\sqrt{95}\). The negative radicand is thus effectively removed from the equation.

It's important to recognize and address negative radicands to correctly perform mathematical operations and simplify expressions. When writing expressions without negative radicands, we ensure they adhere to the standard conventions of complex number arithmetic. This allows for consistent results in both theoretical and practical applications.