To determine which quadrant the complex number [tex]$-14 - 5i$[/tex] is located in on the complex plane, we need to analyze the signs of its real and imaginary parts.
1. Identify the real part: The real part of the complex number is [tex]$-14$[/tex].
2. Identify the imaginary part: The imaginary part of the complex number is [tex]$-5$[/tex] (the term involving the imaginary unit [tex]$i$[/tex]).
Next, use the signs of the real and imaginary parts to determine the quadrant:
- Quadrant I is where both the real and imaginary parts are positive.
- Quadrant II is where the real part is negative and the imaginary part is positive.
- Quadrant III is where both the real and imaginary parts are negative.
- Quadrant IV is where the real part is positive and the imaginary part is negative.
Since the real part ([tex]$-14$[/tex]) is negative and the imaginary part ([tex]$-5$[/tex]) is also negative, the complex number [tex]$-14 - 5i$[/tex] is located in Quadrant III.
Thus, the correct answer is:
III
