The necessity of complex numbers in quantum mechanics was also discussed a while ago in a blog post by Scott Aaronson: https://www.scottaaronson.com/blog/?p=402

The necessity of complex numbers in quantum mechanics was also discussed a while ago in a blog post by Scott Aaronson: https://www.scottaaronson.com/blog/?p=4021 https://www.scottaaronson.com/blog/?p=4021. At the very least, he's able to show the problem with QM described using quaternions: superluminal signalling!