How do you find the distance on a complex plane from 5-12i to the origin?

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How do you find the distance on a complex plane from 5-12i to the origin?

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Answer 1 · 2015-12-29T01:03:00

Calculate its module.

Explanation:

$| z | = \sqrt{x^{2} + y^{2}}$ $absz = sqrt(x^2 + y^2)$ with $x = R e (z)$ $x = Re(z)$ and $y = I m (z)$ $y = Im(z)$ is the distance of $z$ $z$ to the origin (think of $| z |$ $absz$ as $| z - 0 |$ $abs(z - 0)$ ).

So the distance from $5 - 12 i$ $5-12i$ to the origin is $| 5 - 12 i | = \sqrt{5^{2} + {(- 12)}^{2}} = \sqrt{25 + 144} = \sqrt{169}$ $abs(5-12i) = sqrt(5^2 + (-12)^2) = sqrt(25 + 144) = sqrt(169)$

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How do you find the distance on a complex plane from 5-12i to the origin?

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