L2. (a) State, with justification, whether each of the following series converges or diverges. (i)
\sum_(n=1)^(\infty ) (n)/(3n-1)
(ii)
\sum_(==9)^(\infty ) (1)/(lnn)
(iii)
\sum_(n=0)^(\infty ) (n^(4))/(5^(n))
[6 marks] (b) Calculate all fourth roots of
1 i
in C , eqpessing your answers in polar form. [ 6 marks] (c) Use the Cauchy-Riemman equations to determine where the complex function
f
defined by
f(z)=e^(')
is analytic. [8 marks]

Question

L2. (a) State, with justification, whether each of the following series converges or diverges. (i)

\sum_(n=1)^(\infty ) (n)/(3n-1)

(ii)

\sum_(==9)^(\infty ) (1)/(lnn)

(iii)

\sum_(n=0)^(\infty ) (n^(4))/(5^(n))

[6 marks] (b) Calculate all fourth roots of

1 i

in C , eqpessing your answers in polar form. [ 6 marks] (c) Use the Cauchy-Riemman equations to determine where the complex function

f

defined by

f(z)=e^(')

is analytic. [8 marks]

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