Question

How do you find `abs( -5 - 4i )`?

Answer 1

`sqrt41`

Explanation:

Given a complex number z = x + yi , then it's `color(blue)"modulus ( magnitude )"` is found using Pythagoras' theorem.

`color(orange)"Reminder " color(red)(|bar(ul(color(white)(a/a)color(black)(|x+yi|=sqrt(x^2+y^2))color(white)(a/a)|)))`

here x = - 5 and y = -4

`|-5-4i|=sqrt((-5)^2+(-4)^2)=sqrt(25+16)=sqrt41≈6.403" units"`