How Do Complex Number Operations Affect Results?

[Ry122]

How do I express the following in the form a+ib?

$$(\sqrt{-4} - 1) (\sqrt{-9})$$

My attempt:
(2i - 1)(3i)
6i-3i = 3i

 

[StatusX]

Close, but (2i)(3i)=6i²=-6, not 6i.

 

[Ry122]

Can you tell me why the answer -6-+3i has plus or minus 3i?

Also can you tell me the answer to (3+i)^2 - (3+i)^2
The answer I got was 0.
9+6i+i^2-9-6i-i^2=0

 

[Dick]

You have to define what you mean by sqrt(-n) for n>0. You could choose it to be either i*sqrt(n) or -i*sqrt(n). That's your sign ambiguity.

 

[HallsofIvy]

Can you tell me why the answer -6-+3i has plus or minus 3i?

What was that the answer to?? Surely not the (2i-1)(3i) problem you were just talking about!

Also can you tell me the answer to (3+i)^2 - (3+i)^2
The answer I got was 0.
9+6i+i^2-9-6i-i^2=0

The answer to a²- a² is 0 no matter what a is!