To determine which point represents the complex number [tex]\( 3i - 4 \)[/tex], let's break down the components of the complex number step by step.
1. Understanding Complex Numbers:
- A complex number is of the form [tex]\( a + bi \)[/tex], where [tex]\( a \)[/tex] is the real part and [tex]\( bi \)[/tex] is the imaginary part.
2. Identify the Real and Imaginary Parts:
- For the complex number [tex]\( 3i - 4 \)[/tex], we can rewrite it as [tex]\( -4 + 3i \)[/tex].
- Here, the real part [tex]\( a = -4 \)[/tex] and the imaginary part is [tex]\( 3i \)[/tex].
3. Plotting on the Complex Plane:
- The complex plane consists of a horizontal axis (real axis) and a vertical axis (imaginary axis).
- The point representing [tex]\( -4 + 3i \)[/tex] would be located at [tex]\( (-4, 3) \)[/tex].
4. Choosing the Correct Point:
- We look at the given points to see which one corresponds to the coordinates [tex]\( (-4, 3) \)[/tex].
After following these steps, we conclude that the point representing the complex number [tex]\( 3i - 4 \)[/tex] is the answer associated with the coordinate [tex]\( (-4, 3) \)[/tex]. Therefore, the correct point representing the complex number [tex]\( 3i - 4 \)[/tex] is:
C
