Find f(infinity) for the complex function:
f(z) = (iz-5)/(8z+3i)
Thanks,
John
Hmmm. I'd do this by making the denomonator real:
(-5+zi)/(8z+3i) * (8z-3i)/(8z-3i)
= (-5+zi)(8z-3i)/(64z^2+9)
= [(-40z + 3z) + (8z^2-15)i]/(64z^2+9)
= -37z/(64z^2+9) + (8z^2-15)/(64z^2+9) i
Now, as z gets huge, all the small constants vanish, and we get
-37/64z + 1/8 i = 1/8 i