Rotation as Complex Number Multiplication

A two-dimensional vector, such as v = [a, b], can be represented as a single number in the complex plane. This is done by mapping the first component of the vector to the real part of the complex number and the second component to the imaginary part. Given this transformation, which of the following complex numbers correctly represents the vector x = [5, -2]?

When mapping two-dimensional vectors to the complex plane, it is possible for two distinct vectors to be represented by the exact same complex number.

A common method for analyzing vector rotation involves representing two-dimensional vectors as complex numbers. Match each 2D vector on the left with its corresponding representation in the complex plane on the right.