Complex Addition/Examples/(2 + 3i) + (4 - 5i)/Proof 2

Proof

 * Complex-Addition-(2+3i)+(4-5i).png

Let the complex numbers $2 + 3 i$ and $4 - 5 i$ be represented by the points $P_1$ and $P_2$ respectively in the complex plane.

Complete the parallelogram with $OP_1$ and $OP_2$ as the adjacent sides.

By the Geometrical Interpretation of Complex Addition, the point $P$ represents the complex number $6 - 2 i$, which is the sum of $2 + 3 i$ and $4 - 5 i$.