In Hokuro, does $←$ added to $↙$ equal $↙$?

Sorry if any of the info in this question isn't needed, I'm for some reason just really used to putting a lot of info/additional resources into my questions lol.

So as you may or may not know, I recently posted my first Hokuro puzzle.[1] A while after I posted it, I got this comment from @sarsaparilla[2] :

Very cool that you created a hokuro puzzle as well! It seems to be missing clues in R8C3 and R5C7 though?

Okay, so that's my fault. Those are also clues that I accidentally missed when posting the question and after my first edit. However I have a question:

Say I have the directions "west" $$←$$ and "southwest" $$↙$$. If I add them together, would I get\begin{align}\text{directions version:}&\quad←+↙\,=\,←+←+↓\,=\,↙\\\text{text directions version:}&\quad\text{west}+\text{southwest}=\text{west}+\text{west}+\text{south}=\text{southwest}\end{align}or what would I do to add those two directions together, or is my Hokuro puzzle immediately invalid if I have to add those directions together?

Notes

[1]

For those who didn't know (will edit out if unneeded):

1. Hokuro was first created on December 2nd, 2020 as an entry for Fortnightly Topic Challenge #44: Introduce a new grid deduction genre to the community. (The official introduction to Hokuro was the highest voted out of the 14 new genres with a total of 25 votes and 2nd most viewed with 668 views by the end of the fortnight.) [Source]
2. Hokuro is short for 方向クロス (romaji: hōkō kurosu) which is gotten by translating "direction cross" from English to Japanese. (easily confirmable using DeepL Translate, romaji originally gotten using Google Translate)