Pardon the handwriting, please.

is the answer | z | = 25, pie = 1.85?

Haha Yes, the answer is indeed that. Don't know why exactly I got downvoted here when I try not to feed students answers, but if you're in doubt, you can also check on wolframalpha by typing arg(-7+24i) and mod(-7+24i), or watch the below video for better understanding of the concept:

https://www.youtube.com/watch?v=61gSsgrx4vs