Which one of the following is the real part of the complex number: 6(2-3i)?A.2B.12C.-3D.6

Break Down the Problem

1. Identify the given complex number: $6(2 - 3i)$.
2. Recognize the structure of a complex number $a + bi$ where $a$ is the real part.

Relevant Concepts

1. A complex number in the form $a + bi$ can be simplified by distributing the coefficients.
2. The real part is the coefficient of the real unit, while the imaginary part is the coefficient of $i$.

Analysis and Detail

1. Expand the expression: $6(2 - 3i) = 6 \cdot 2 - 6 \cdot 3i$
2. Calculate each part: $= 12 - 18i$
3. Identify the real part:
   • Here, $12$ is the real part, and $-18i$ is the imaginary part.

Verify and Summarize

• The only number in the complex expression that is not multiplied by $i$ is $12$.
• The correct identification reveals that $12$ is indeed the real part of the complex number.

Final Answer

Thus, the real part of the complex number $6(2 - 3i)$ is B. 12.