Algebra 101, and some about complex numbers

[Keba]

1. The problem statement, all variables and given/known data
I was looking up complex numbers and the guy on YouTube made something similar to this equation:
i=-1
c^2-(d^2*i^2) = c^2+d^2

(http://www.youtube.com/watch?v=bPqB9a1uk_8 - 2:55)

2. Relevant equations
I do not understand why it is "c^2+d^2" and not "c^2-d^2"
I would like a detailed explanation, as I might have misunderstood algebra somehow

3. The attempt at a solution
I would do this to find a solution
c^2-(d^2*i^2)
c^2-(d^2*(-1)^2)
c^2-(d^2*1)
c^2-d^2

[sutupidmath]

The general form of a complex nr is ;a+bi, where i is the imaginary.

it is the square root of negative one, that is:

\sqrt{-1}=i=>i^2=-1 now going back to what u have there

c^2-(d^2i^2)=c^2-(d^2(-1))=c^2+d^2

[Keba]

I see, so my problem wasn't with algebra but with my understanding of complex numbers.
Then it makes perfect sense! I thank you good sir =P

[HallsofIvy]

1. The problem statement, all variables and given/known data
I was looking up complex numbers and the guy on YouTube made something similar to this equation:
i=-1
Here was your error. i is NOT -1. Its square is -1: i2= -1.

c^2-(d^2*i^2) = c^2+d^2

(http://www.youtube.com/watch?v=bPqB9a1uk_8 - 2:55)

2. Relevant equations
I do not understand why it is "c^2+d^2" and not "c^2-d^2"
I would like a detailed explanation, as I might have misunderstood algebra somehow

3. The attempt at a solution
I would do this to find a solution
c^2-(d^2*i^2)
c^2-(d^2*(-1)^2)
c^2-(d^2*1)
c^2-d^2