In which quadrant is the number –14 – 5i located on the complex plane?

General
1

in which quadrant is the number –14 – 5i located on the complex plane?

2

In which quadrant is the number –14 – 5i located on the complex plane?

Answer: To determine the quadrant in which the complex number -14 - 5i is located on the complex plane, we need to analyze the signs of its real and imaginary parts.

A complex number is generally written in the form a + bi, where a is the real part and b is the imaginary part.

For the complex number -14 - 5i:

  • The real part a is -14.
  • The imaginary part b is -5.

The complex plane is divided into four quadrants:

  1. First Quadrant (I): Both the real part and the imaginary part are positive (a > 0 and b > 0).
  2. Second Quadrant (II): The real part is negative, and the imaginary part is positive (a < 0 and b > 0).
  3. Third Quadrant (III): Both the real part and the imaginary part are negative (a < 0 and b < 0).
  4. Fourth Quadrant (IV): The real part is positive, and the imaginary part is negative (a > 0 and b < 0).

Given that -14 is negative and -5 is also negative, the complex number -14 - 5i falls into the Third Quadrant (III).

Therefore, the number -14 - 5i is located in the Third Quadrant on the complex plane.