# Complex Addition/Examples/Travel 1/Proof 2

Jump to navigation
Jump to search

## 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: $18 \ \text {(b)}$