Complex Addition/Examples

Examples of Complex Addition

Example: $\paren {3 + 2 i} + \paren {5 + 6 i}$

$\paren {3 + 2 i} + \paren {5 + 6 i} = 8 + 8 i$

Example: $\paren {-1 + 4 i} + \paren {2 + \paren {-7} i}$

$\paren {-1 + 4 i} + \paren {2 + \paren {-7} i} = 1 + \paren {-3} i$

Example: $\paren {3 + 4 i} + \paren {5 + 2 i}$

$\paren {3 + 4 i} + \paren {5 + 2 i} = 8 + 6 i$

Example: $\paren {4 - 3 i} + \paren {2 i - 8}$

$\paren {4 - 3 i} + \paren {2 i - 8} = -4 - i$

Example: $\paren {-3 + 5 i} + \paren {4 + 2 i} + \paren {5 - 3 i} + \paren {-4 - 6 i}$

$\paren {-3 + 5 i} + \paren {4 + 2 i} + \paren {5 - 3 i} + \paren {-4 - 6 i} = 2 - 2 i$

Example: $\paren {2 + 3 i} + \paren {4 - 5 i}$

$\paren {2 + 3 i} + \paren {4 - 5 i} = 6 - 2 i$

Example of Travel: $1$

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.

Example of Travel: $2$

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.