a level further maths exam with answers

a level further maths exam with answers


2cos0 - CORRECT ANSWERS ✔✔z + 1/z


2isin0 - CORRECT ANSWERS ✔✔z - 1/z


2cosn0 - CORRECT ANSWERS ✔✔z^n + 1/z^n


2isinn0 - CORRECT ANSWERS ✔✔z^n - 1/z^n


0 - CORRECT ANSWERS ✔✔e^ipi + 1


1 - e^i0 - CORRECT ANSWERS ✔✔-2isin(0/2)e^(0i/2)


1 + e^i0 - CORRECT ANSWERS ✔✔2cos(0/2)e^(0i/2)


z^n - CORRECT ANSWERS ✔✔r(cos(0 + 2kpi) + isin(0+2kpi))


0 - CORRECT ANSWERS ✔✔sum of the nth roots of a complex
number

, 1/root(x^2-1) - CORRECT ANSWERS ✔✔differential of cosh^-1x


1/1-x^2 - CORRECT ANSWERS ✔✔differential of tanh^-1x


critical damping - CORRECT ANSWERS ✔✔1) dicriminant of
auxillary equation is 0 (repeated root)
2) comes to rest without oscillating


particular function (sub into initial equation by differentiating twice)
- CORRECT ANSWERS ✔✔non homogenous differential equation


y = Pcosbx + Qsinbx - CORRECT ANSWERS ✔✔pure complex roots
(differential equation)


y = e^ax (Pcosbx + Qsinbx) - CORRECT ANSWERS ✔✔complex
roots (differential equation)


rcos0 - CORRECT ANSWERS ✔✔x (polar coordinates)


rsin0 - CORRECT ANSWERS ✔✔y (polar coordinates)