Answered

IDNLearn.com connects you with a global community of knowledgeable individuals. Join our knowledgeable community to find the answers you need for any topic or issue.

In which quadrant is the number [tex]\(-14 - 5i\)[/tex] located on the complex plane?

A. I
B. II
C. III
D. IV

Sagot :

GinnyAnsweridn
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.
Thank you for using this platform to share and learn. Don't hesitate to keep asking and answering. We value every contribution you make. For clear and precise answers, choose IDNLearn.com. Thanks for stopping by, and come back soon for more valuable insights.