Discovery -- Revealing the existence of imaginary numbers in real life
Vectors are ubiquitous in the real world via physical quantities such as position, velocity, acceleration and force. Real numbers can stretch vectors through multiplication. By analogy, rotational numbers are introduced to rotate vectors through multiplication as well. A fundamental equation of position vector rotation is then found with an orthogonal rotational number of angle /2 natively appearing in it, which results in a novel development of complex numbers and Euler’s formula without using and relying on or . The existence of a rotational number set is also discovered as a consequence with one of its members, the orthogonal rotational number having the property and being equivalent to the imaginary unit. This has finally revealed imaginary numbers in our daily life after 500 years since the inception in 1520s.