Question

For the complex number z = negative startfraction startroot 21 endroot over 2 endfraction minus startfraction startroot 7 endroot over 2 endfraction i, what is arg(z)?.

Answer 1

Answer: B. 210°

Explanation:

Answer 2

arg(z) = 7π/6

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 ...

`z=-(√(21))/(2)-(√(7))/(2)i=(√(7))/(2)(-√(3)-i)\\\\\arg{(z)}=\arctan{(-1)/(-√(3))}\\\\\boxed{\arg{(z)}=(7\pi)/(6)}`