Me i do not understand this rule

i have to simplify *

the actual answer came up to 4xiyi

but i got 4ixyi

i don't understand how the actual answer did not include the absolute value for the x either. it's so annoying because the rule said that absolute values are for odd variables if n is even on roots and powers. well the answer does not have absolute values on that x which is odd at ! and that is the actual answer. i don't get it

40*x*IyI*sqrt(3)

Step-by-step explanation:

I believe you know how to multiply these out so I don't have to explain that.  The reason why there is no absolute value sign on x is a bit tricky to understand.

By definition:

sqrt(a^2) = IaI

So that explains why "y" is in absolute value.

The reason why "x" isn't is because we don't technically have:

sqrt(x^2)

We have:

sqrt(x)*sqrt(x)

And by definition:

sqrt(a)*sqrt(a) = a

So that's why "x" isn't in absolute value.

it would rotate about 180 degrees.