Imagining numbers (particularly the square root of minus fifteen)

This is a book about the imagination in general and about the mathematical imagination in particular.

Barry Mazur considers the range of our imaginative experiences.

When we read a line of poetry - "The yellow of the tulip" - what is it we experience in the mind's eye? And when we imagine a number, in particular an impossible number such as the square root of a negative quantity, what imaginative object might this bring to mind?