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

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Answer 1 · 2018-03-09T20:59:42

$abs(1+3i) = sqrt(10)$

The absolute value of a complex number is its distance from the origin $0$ 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:

$abs(1+3i) = sqrt(1^2+3^2) = sqrt(1+9) = sqrt(10)$

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