If real numbers run on a left to right axis, imaginary numbers run up and down. They allow for negative answers to multiplication, for example -2 times -2 equals 4, but i2 times i2 equals -4. Scientists use these numbers to deal with difficult mathematics where real numbers won’t do the job, for example calculating the sum over histories of a particle.
Imaginary numbers/time Term Timeline in A Brief History of Time
The timeline below shows where the term Imaginary numbers/time appears in A Brief History of Time. The colored dots and icons indicate which themes are associated with that appearance.
...possible path. Scientists know how to measure this, but actually doing the math requires using imaginary numbers . This is a normal mathematical tool, by which numbers can be multiplied against themselves... (full context)