# What is the distance between the following polar coordinates?:  (2,(11pi)/8), (19,(3pi)/8)

Distance is $21$.
A polar coordinates for two points are $\left(2 , \frac{11 \pi}{8}\right)$ and $\left(19 , \frac{3 \pi}{8}\right)$.
The argument of first is $\frac{11 \pi}{8}$ and other is $\frac{3 \pi}{8}$. The difference between them is $\frac{11 \pi - 3 \pi}{8} = \pi$ and hence one point is directly opposite the other across origin on the Argand plane.
Hence distance between two points is $2 + 19 = 21$