Complex Addition/Examples/Travel 1/Proof 2
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Example of Complex Addition
A man travels:
- $12$ kilometres northeast
then:
- $20$ kilometres $30 \degrees$ west of north
then:
- $18$ 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.
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: Solved Problems: Polar Form of Complex Numbers: $18 \ \text {(b)}$