Let's determine in which quadrant the complex number [tex]\(-14 - 5i\)[/tex] is located on the complex plane.
A complex number is typically written in the form [tex]\(a + bi\)[/tex], where [tex]\(a\)[/tex] represents the real part and [tex]\(b\)[/tex] represents the imaginary part. In this case, [tex]\(a = -14\)[/tex] and [tex]\(b = -5\)[/tex].
To determine the quadrant, we need to examine the signs of the real part [tex]\(a\)[/tex] and the imaginary part [tex]\(b\)[/tex]:
1. Quadrant I: Both the real part and the imaginary part are positive ([tex]\(a > 0\)[/tex] and [tex]\(b > 0\)[/tex]).
2. Quadrant II: The real part is negative, and the imaginary part is positive ([tex]\(a < 0\)[/tex] and [tex]\(b > 0\)[/tex]).
3. Quadrant III: Both the real part and the imaginary part are negative ([tex]\(a < 0\)[/tex] and [tex]\(b < 0\)[/tex]).
4. Quadrant IV: The real part is positive, and the imaginary part is negative ([tex]\(a > 0\)[/tex] and [tex]\(b < 0\)[/tex]).
Given the number [tex]\(-14 - 5i\)[/tex]:
- The real part [tex]\(a = -14\)[/tex] is negative.
- The imaginary part [tex]\(b = -5\)[/tex] is also negative.
According to the quadrant definitions, if both [tex]\(a\)[/tex] and [tex]\(b\)[/tex] are negative, the complex number is located in Quadrant III.
Thus, the number [tex]\(-14 - 5i\)[/tex] is located in Quadrant III.
