Question 1078278
<pre>
{{{(z - 3)^4 + (z - 5)^4}}}{{{""=""}}}{{{-8}}}

{{{(z - 3)^4 + (z - 5)^4+8}}}{{{""=""}}}{{{0}}}

The average of z-3 and z-5 is z-4, 
so let w = z-4, i.e., z = w+4

{{{(w+4 - 3)^4 + (w+4 - 5)^4+8}}}{{{""=""}}}{{{0}}}

{{{(w+1)^4 + (w-1)^4+8}}}{{{""=""}}}{{{0}}}

{{{w^4+4w^3+6w^2+4w+1+w^4-4w^3+6w^2-4w+1+8}}}{{{""=""}}}{{{0}}}

{{{2w^4+12w^2+10}}}{{{""=""}}}{{{0}}}

Divide through by 2

{{{w^4+6w^2+5}}}{{{""=""}}}{{{0}}}

{{{(w^2+5)(w^2+1)}}}{{{""=""}}}{{{0}}}

{{{matrix(5,5,

w^2+5=0,";","","",w^2+1=0,
w^2=-5,  ";","","",w^2=-1,
w=""+-sqrt(5)i,";","","",w=""+-i,
z-4=""+-sqrt(5)i,";","","",z-4=""+-i,
z=4+-sqrt(5)i,";","","",z=4+-i

)}}}

Edwin</pre>