Why: OC=OB+BC of an equilateral triangle?

Question

Let's suppose that we have an equilateral triangle ABC as complex numbers. Then why is OC = OB+BC?

Isn't OC the shortest distance from O to C? OB+BC is longer right?

Answer 1

The vectors satisfy $\overrightarrow{OC}=\overrightarrow{OB}+\overrightarrow{BC}$, but their magnitudes satisfy $OC<OB+BC$. The complex numbers are representations of the vectors, not the magnitudes.