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

Proof

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

Let the complex numbers $3 + 4 i$ and $5 + 2 i$ 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 $8 + 6 i$, which is the sum of $3 + 4 i$ and $5 + 2 i$.