Let $u = −1 − 10i$ and $v = −2 + 7i$.

1. What are the modulus and argument of $u$?

   Step (a):

   $|u|=\sqrt{(-1)^2+(-10)^2}\:\:\:\:\:\:\arg(u)=\tan^{-1}\left(\frac{7}{-2}\right)$

2. Use $\overline { v }$ to compute the modulus of $v$.

   Hint (b):

   $|v|=\sqrt{ |v|v}$

3. What is the distance between $u$ and $v$ in the complex plane?

   Hint (c):

   $|u-v|$

4. Where is the midpoint of the segment joining $u$ and $v$ in the complex plane?

   Hint (d):

   $\frac{u+v}{2}$