What are these laws and how do they fit into mathematics? I am having trouble understanding them...

You mean the trigonometric identities?

It's been a while, but I think:

1xa=a

0xa=0

a+b=b+a

I'm not sure, this is what my textbook says:

 

Identity Laws

There is a unique number 0 with the property that 0+a = a+0 = a

There is a unique number 1 with the property that 1*a = a*1 =a

 

I have no idea what that means....

By the way i'm not very good at maths so a simple explanation would be appreciated...

The first one:

"There is a unique number 0 with the property that 0+a = a+0 = a"

It's simply saying that if you add 0 to any number, you get that number. 4 + 0 = 4.

 

Second one:

"There is a unique number 1 with the property that 1*a = a*1 =a"

If you multiply anything by 1, you get the same number you started with. 5 * 1 = 5.

Thank you for explaining it so well

 

I must seem really stupid...

 

Could someone also help me with what complex numbers are?

I'd just like to say that the uniqueness properties are important, too. Because, if there were two zeros, 0 and 0', there are a bunch of properties that start to crumble. 4 - 4 = 0 or =0'? How do you know which one to use? And, if there aren't unique answers to simple arithmetic, it's just going to get worse trying to build on it. So, it is important that there is a 0, and that there is a unique 0, same thing about 1.