Complex Addition/Examples/Travel 1/Proof 2

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Example of Complex Addition

A man travels:

$12$ kilometres northeast


$20$ kilometres $30 \degrees$ west of north


$18$ kilometres $60 \degrees$ south of west.

Assuming the curvature of the Earth to be negligible at this scale, at the end of this travel, he is $14.7$ kilometres in a direction $45 \degrees 49'$ west of north from his starting point.


By plotting the points in a graphics package, or on paper with a ruler and protractor:

Travel Example.png