Find out how the quaternion function G(v) = qvq^-1 gives a simple
algebraic method for working with rotations in 3-space.
See how 4 dimensional quaternions involve vectors in 3-space and
how the quaternion function F(v) = nvn gives a simple algebraic
method of working with reflections in planes in 3-space.
To do this problem you only need to know how to add and multiply two by two matrices. The problem gives models for complex numbers and 4-dimensional numbers called quaternions. Although you don't need the information to do this problem you may like to read the NRICH article
What are Complex Numbers?
and the Plus article: