How do you find the absolute value of $1 + 3 i$ $1+3i$ ?

Question

11214 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-03-09T20:59:42

$| 1 + 3 i | = \sqrt{10}$ $abs(1+3i) = sqrt(10)$

The absolute value of a complex number is its distance from the origin $0$ $0$ in the complex plane.

By Pythagoras' theorem this is the square root of the sum of the squares of the real and imaginary parts.

That is:

$| 1 + 3 i | = \sqrt{1^{2} + 3^{2}} = \sqrt{1 + 9} = \sqrt{10}$ $abs(1+3i) = sqrt(1^2+3^2) = sqrt(1+9) = sqrt(10)$

How do you find the absolute value of 1+3i1+3i?