In this novel, Sarah is abducted by a group of other "cuckoos" who want her to use her for their own purposes, purposes which would likely result in the end of all life on Earth. (Not only human life would be endangered, but also all of the other sentient species that inhabit the planet in this series, including religiously devout little creature that look like field mice, monkey-like furis, incubi and succubi).

Now, let's talk about math.

The title of this book, the cover (which features cool blue mathematical formulas), and the mathematical expression reprinted on the first page of every chapter (which appears to be an approximation of the number of twin primes less than n for no particular reason) all had me expecting that math would play a very big role in this book. I know, I'm guilty of judging a book by its cover, but that's what it led me to believe.

In the first half of the book math just appears to be a personal interest of Sarah's that essentially functions as a security blanket ("prime numbers are some of the most soothing things in the universe...they're always the same, perfect, calming constants that don't change, don't vary no matter how much everything else gets twisted on itself") and a source of lame metaphors ("things that changed everything around them, like a new variable introduced to a formerly stable equation"). We are told over and over how reliable and safe numbers feel to her. She recites prime numbers to herself in times of stress. If you combine this with the fact that she has trouble reading emotions and body language and that she has to work hard to behave normally in social interactions, this comes together to form a rather standard stereotype of mathematical fiction: the autistic mathematical savant. Of course, she also happens to be a psychic insect from another dimension, which doesn't fit the trope, but aside from that these features are very recognizable. I found all of this very disappointing for several reasons. First, it seemed that my initial expectations about math playing a significant role in this book were not correct. Secondly, I consider reliance on such tired stereotypes to indicate very lazy writing on the part of the author. Finally, I fear that those stereotypes reinforce false beliefs about both mathematics and autism.

In the second half of the book, however, the role of mathematics changes drastically. It stops being grade school arithmetic used to provide comfort and becomes math that is important, but too vague to understand. We know that Sarah has to do something with an equation, an equation that is too big, and that the fate of the world hangs in the balance. It is not clear what sort of equation it is. (We are told that it involves numbers and letters.) It also isn't clear what she is doing with the equation. Sometimes it sounds like she has to "balance" it, other times as if she has to "solve" it...or does she just need to understand it? And, the author cannot really explain what makes this equation so difficult for her:

The math in this book is not sophisticated. But then, nothing in this book is. The descriptions of the different species, the moral ambiguity, and the twee romance between Sarah and her incubus (adopted) cousin are all presented at a maturity level I would consider suitable only for the "young adult" genre.

Imaginary Numbers ends suddenly on a cliffhanger which is resolved in the sequel Calculated Risks (2021).