How do you find abs( x+iy )?

1 Answer
Mar 21, 2016

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

Explanation:

abs(x+iy) is essentially the distance between 0 and x+iy in the Complex plane.

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

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

Notice that (x+iy)(x-iy) = x^2-i^2y^2 = x^2+y^2

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 z into Real and imaginary parts, we can say:

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