# Complex Addition/Examples/Travel 2/Proof 2

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## Example of Complex Addition

An airplane travels:

$150$ kilometres southeast

then:

$100$ kilometres due west

then:

$225$ kilometres $30 \degrees$ north of east

then:

$323$ kilometres northeast.

Assuming the curvature of Earth to be negligible at this scale, at the end of this travel, the plane is $490$ kilometres in a direction $28.7 \degrees$ north of east from its starting point.

## Proof

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

$\blacksquare$