# Question #af849

Jul 21, 2015

$\arctan \left(\frac{7}{3}\right) - \pi \setminus \approx - 1.976 \setminus m b \otimes \left\{r a \mathrm{di} a n s\right\} \setminus \approx - {113.2}^{\setminus \circ}$

#### Explanation:

First, mark the point $- \left(3 + 7 i\right) = - 3 - 7 i$ in the complex plane. Note that it is in the 3rd quadrant. This means that its argument, or angle (typically taken to be between $- \pi$ and $\pi$) is $\arctan \left(\frac{- 7}{- 3}\right) - \pi = \arctan \left(\frac{7}{3}\right) - \pi \setminus \approx - 1.976 \setminus m b \otimes \left\{r a \mathrm{di} a n s\right\} \setminus \approx - {113.2}^{\setminus \circ}$.

You need to subtract $\pi$ from $\arctan \left(\frac{y}{x}\right)$ in this case because of the fact that the point is in the 3rd quadrant. The arctangent function gives an output between $- \frac{\pi}{2}$ and $\frac{\pi}{2}$ radians.

Jul 22, 2015

The answer already given is perfectly alright.

#### Explanation:

Just to make it more clear, it can be stated that argument is measured in anticlockwise direction from positive x axis and it is positive till it is less than 180 degrees. In this case the angle that vector -3-7i makes with x axis is in the third quadrant, hence more than 180 degrees. In this case the angle is measured in clockwise direction , hence it is -1.976 radians.