Home > PC3 > Chapter 11 > Lesson 11.2.1 > Problem11-87

11-87.

Let $u = −1 − 10i$ and $v = −2 + 7i$.

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

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

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

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

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

$|u-v|$

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

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