# A word becomes imaginary

I'm important in geometry
If you add a letter, you get the German translation
If you re-order the letters of the English word and add brackets () and multiply, it becomes imaginary
If you re-order the letters of the German word and add brackets () and multiply, it becomes real

Find the word with the above properties.

• What's "Englisch"? – Scratch---Cat Aug 2 '20 at 10:05
• It's a typo - I corrected it – ThomasL Aug 2 '20 at 13:03

A line!

This is because

1. Lines are quite important in geometry...

2. linie is the German translation of "line"

3. $$i \cdot \ln(e)=i$$ which is imaginary

4. $$i \cdot i \cdot \ln(e)=-1$$ which is real!

• perfect answer! – ThomasL Aug 1 '20 at 21:10