# How do you find #abs( x+iy )#?

##### 1 Answer

Mar 21, 2016

#### Explanation:

Using the distance formula which comes from Pythagoras theorem, we have:

#abs(x+iy) = sqrt(x^2+y^2)#

Notice that

So another way of expressing this is:

#abs(x+iy) = sqrt((x+iy)(x-iy)) = sqrt((x+iy)bar((x+iy)))#

So without explicitly splitting a Complex number

#abs(z) = sqrt(z bar(z))#