Math
posted by Nayla .
Does (7/4i1) symplify to be 7(1+4i)/18

Not quite. Your parenthese seem to be in the wrong place, and your math is wrong.
7/(4i1)= 7(4i+1)/[(4i+1)(4i1)]
= 7(4i +1)/(17)
= (7/17)(1+4i) 
These are complex numbers by the way.

Thanks

why is the 1+4i on the side of the fraction and not on the top with the 7

(7/17)(1+4i) is the same as 7(1+4i)/17.
I too think it is simpler to write it as DRWS did, where the numeric fraction precedes the algebraic part. 
is (7/17)(28/17i) the same thing

"is (7/17)(28/17i) the same thing "
No it is not.
(7/17)*(1+4i)
=(7/17)*1 + (7/17)*4i
=(7/17) + 28i/17
But this is not a simplified version.
In any case the object is to remove the "i" from denominator, or "rationalizing the denominator". Some teachers may consider it incomplete if squareroot signs or "i" appear in the denominator.
The reason that the numerator and denominator were multiplied by (1+4i) was to create the product (1+4i)*(14i)=17 in the denominator, thereby rationalizing it.