Question

in what quadrant of an argand diagram should - 1/3 - 11i be plotted? write your answer with a number instead of a roman numeral. (1 point)

Explanation:

Step1: Recall the form of complex - number in Argand diagram

In an Argand diagram, a complex number \(z = a+bi\) is plotted with the real - part \(a\) on the x - axis and the imaginary part \(b\) on the y - axis. For the complex number \(z=-\frac{1}{3}-11i\), the real part \(a =-\frac{1}{3}\) and the imaginary part \(b=- 11\).

Step2: Determine the quadrant based on the signs of real and imaginary parts

In the coordinate system, if \(a\lt0\) and \(b\lt0\), the point \((a,b)\) lies in the third quadrant. Since the real part \(a =-\frac{1}{3}\lt0\) and the imaginary part \(b = - 11\lt0\), the complex number \(z=-\frac{1}{3}-11i\) is plotted in the third quadrant.

Answer:

Third