I Don't Know What Is This Subject Called In English But It's About Complex Numbers

Question

it says

25 = 16 - 9 i^2 = (4 ± 3i)

But My Teacher Says

25 = 25 - 0 i^2 = (5 ± 0i)

I Think My Teacher Is Wrong , The Result Is 25 But There Will Not Be Complex Number Because ( 0i = 0)
So Is My Teacher Wrong Or Not ?

Answer 1

both end statements are incorrect

(4 ± 3i) means (4+3i) OR (4-3i)
it has nothing to do with the multiplication of
(4+3i)(4-3i)

which would be
16 - 9i^2
= 16 - (-9)
= 25

your teacher should have said, (probably did)
(5 + 0i)(5-0i)
= 25 - 0i^2
= 25