1. Determine if E (/sum) ∞ to n=1(e^n/1000)^n converges.
2. If f(x) = E(/sum) infinity to k=1 (cos^2 x^k) determine f(pi/4).
3. Determine if E(/sum) infinity to n=1 1/3 sqrt 8n^2-5n converges.
4. Determine if E(/sum) infinity to n=1 (n!/n^n) converges.
5. z=1+3i evaluate z* and |z|.
6. Put in x + iy form 1+4i/4+3i.
7. Put z = 1 + √3i in polar form.
8. Evaluate ln(e(1 + √3i)); show all solutions.
9. Find the 4th root of z = 8(1−√3i). Define θ where z = reiθ and θ′ which
is the angle between each solution. Draw the solutions on the complex
plane.
#1. clearly not, since all the numbers are greater than 1. I suspect you are missing a minus sign somewhere
#2. Not clear. If you meant (cos^2 x)^k then it's just a geometric series. cos^2(x^k) diverges
#3. again unclear. If you meant 1/3 * √(8n^2-5n) then that clearly diverges.
If you meant 1/(3√(8n^2-5n)) then it also diverges, since for very large n, that grows as 1/n, the harmonic series
#4. It converges, since for large enough n, n! < n^n
#5. z* = 1-3i, |z| = √(1^2+3^2) = √10
How about you do some now?