Question

How do you find `abs( sqrt11 + i sqrt(5))`?

Answer 1

Use the definition of a modulus `|a+bi| = sqrt(a^2+b^2)` to find that

`|sqrt(11)+sqrt(5)i|=4`

Explanation:

Given a complex number `a+bi`, the modulus of that number, denoted `|a+bi|`, is given by

`|a+bi| = sqrt(a^2+b^2)`

This is analogous to the absolute value of a real number, giving the distance of the complex number from the origin on the complex plane, rather than the distance from `0` on the number line.

For our given value, then, we have

`|sqrt(11)+sqrt(5)i| = sqrt((sqrt(11))^2+(sqrt(5))^2)`

`=sqrt(11+5)`

`=sqrt(16)`

`=4`