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The distributive property is a fundamental arithmetic rule which allows us to multiply a single term by each term inside a parenthesis. When using the distributive property to multiply complex numbers, it helps to view the complex expression just like a regular arithmetic problem.

In our example, we needed to multiply \( -7i \) by \( (3 + 4i) \). Applying the distributive property, we break it down to \( -7i(3) + (-7i)(4i) \). This makes it easier to handle the multiplication step-by-step.

It's important to correctly apply the distributive property before performing the actual multiplications. Misapplying the property can lead to errors in solving the problem, so consistently practice this with simpler problems to get comfortable.

The imaginary unit, denoted as \( i \), is a mathematical concept used to extend the concept of numbers. The imaginary unit is defined by the property \( i^2 = -1 \). This differs from real numbers, where square values are always positive.

Imaginary numbers are numbers in the form of \( bi \) where \( b \) is a real number. When multiplying complex numbers, remembering the key feature of \( i^2 \) will allow for proper simplification of the result.

For instance, in the step where \( -7i \) was multiplied by \( 4i \), we used the property that \( i^2 = -1 \). This is how \( -28 i^2 \) was simplified to \( 28 \). Properly utilizing the imaginary unit concept is crucial in handling the multiplication and simplification of complex numbers.

The standard form of a complex number is written as \( a + bi \), where \( a \) represents the real part and \( b \) represents the imaginary part.

After performing operations on complex numbers, it is common practice to rearrange the result into this form. This enables ease of interpretation and further mathematical operations. In our solution, the resultant expression from multiplying and simplifying was rearranged to \( 28 - 21i \).

Always make sure to write your final answer in this standard form. This practice provides clarity and aligns with conventional mathematical representation of complex numbers.