# 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:

$\blacksquare$

## Sources

- 1981: Murray R. Spiegel:
*Theory and Problems of Complex Variables*(SI ed.) ... (previous) ... (next): $1$: Complex Numbers: Supplementary Problems: Polar Form of Complex Numbers: $85 \ \text {(b)}$