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: $85 \ \text {(b)}$