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In the realm of mathematics, complex numbers play a crucial role in extending our numerical system. They allow us to find solutions to equations that don't have real number answers. The standard form of a complex number is written as A + Bi, where A represents the real part and Bi represents the imaginary part, with i being the imaginary unit satisfying the equation i^2 = -1.

In the given exercise, the end goal is to present the result as a complex number in standard form. To reach this goal, it is fundamental to manipulate the given expression step by step until we can clearly identify the real part and the imaginary part separated by a plus or minus sign, right before presenting the final answer as (-1 - 5i), which adheres to the standard form convention.

Complex conjugates are a powerful tool when dealing with complex numbers, especially when you need to simplify expressions involving division. A complex conjugate of a complex number is formed by changing the sign of the imaginary part. So, the conjugate of 1 + i is 1 - i, and vice versa. Multiplying a complex number by its conjugate eliminates the imaginary part in the denominator, making the expression easier to work with.

In the step-by-step solution, complex conjugates were used to normalize the denominators of the fractions. By doing so, we turned the denominator into a real number, which is crucial for further simplification. This step reflects an essential property of complex conjugates: (a + bi)(a - bi) = a^2 + b^2, a product that is always a real number.

Simplification of complex expressions involves a sequence of strategic steps to reach a form that is easy to interpret—typically the standard form. Simplifying complex expressions is not just about applying operations; it's also about understanding the properties of complex numbers and how to efficiently use them.

The exercise demonstrates simplification through multiplication, expansion of brackets, and combination of like terms. Through these steps, we ensure that we handle real and imaginary parts separately and combine them only at the end. Being methodical is key: multiply first, simplify next, then organize the terms. This process transforms complex expressions, often seemingly convoluted, into a neat standard form. The subtraction and combination of like terms, as seen in the solution -1 - 5i, is the final part of the simplification process, revealing the clarity of the final result.