Calculating z/w in polar form

Calculating z/w in polar form

So we have:
z = 7 + 4i
w = 8-i
I did this: $$7+4i/8-i$$ $$conjagate =\space 8+i$$ Multiply $$z/w \space
by\space conjugate$$ and this is what I got using algebra:
$$52/65\times39i$$
This is what I got using polar form:
$$(2072/257)*(cos(14/27)+i*sin(14/27))=z$$
$$(2024/255)*(cos(-241/1938)+i*sin(-241/1938)) = w$$ $$z/w = 2794/399 +
507/515i$$
Why are they not the same?