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Understanding the standard form of a complex number is essential for performing operations like division. Every complex number can be expressed in the form of a + bi, where a represents the real part and bi represents the imaginary part, with i being the imaginary unit satisfying i^2 = -1. This notation allows us to easily distinguish between the real and imaginary components and perform arithmetic.

For example, the complex number 3 + 4i has a real part of 3 and an imaginary part of 4. In the context of the given exercise, after simplifying the fraction, we obtain the expression in standard form as 0.875 - 0.75i, which clearly separates the real part, 0.875, and the imaginary part, -0.75i.

The conjugate of a complex number is a valuable tool, particularly in division. The conjugate of a complex number a + bi is a - bi. Multiplying a complex number by its conjugate results in a real number because when (a + bi) is multiplied by its conjugate (a - bi), the imaginary parts cancel out, and we are left with a^2 + b^2, which is always real.

In our exercise, we multiplied the numerator and denominator of the fraction by the conjugate of the denominator to eliminate the imaginary part from the denominator. This process transformed our division problem into a form that can be easily simplified using real numbers, ultimately allowing us to express the result in the standard form.

When dealing with complex fractions, the objective is to simplify the expression so that no imaginary unit 'i' remains in the denominator. This process usually involves multiplying the numerator and the denominator by the complex conjugate of the denominator as we discussed. After this multiplication, we simplify the expression by combining like terms and substituting i^2 with -1, as per the definition of the imaginary unit.

Furthermore, we divide both the real and the imaginary part of the numerator by the denominator to achieve the standard form. In our given example, the final step was to divide each term by 64 to simplify our complex fraction to 0.875 - 0.75i, which is a much more manageable form for further operations or interpretation.