Answer:
arg(z) = 7π/6
Step-by-step explanation:
You want the argument of the complex number -√21/2 -√7/2i.
Argument
The argument of the complex number is the angle it makes with respect to the positive real axis. It can be found using the arctangent function, paying attention to quadrant.
The number can be written as ...
[tex]z=-\dfrac{\sqrt{21}}{2}-\dfrac{\sqrt{7}}{2}i=\dfrac{\sqrt{7}}{2}(-\sqrt{3}-i)\\\\\arg{(z)}=\arctan{\dfrac{-1}{-\sqrt{3}}}\\\\\boxed{\arg{(z)}=\dfrac{7\pi}{6}}[/tex]
