nacho said:Please refer to the attached image.
How do I do these questions, In particular
1a, 1c and 1f.
Could anyone give me a hint to get me started with either of these?
Thanks.
nacho said:Thanks for that.
Although, for
1a) it says that the sum of the series is
$\frac{1}{1-\frac{i}{3}}$ $ = $ $\frac{9+3i}{10}$
Why is this? I am unsure how they get to the first term of $\frac{1}{1-\frac{i}{3}}$
Chris L T521 said:Note that
\[\frac{1}{1-\dfrac{i}{3}} = \frac{3}{3\left(1-\dfrac{i}{3}\right)} = \frac{3}{3-i}\]
Now conjugate and you'll get the desired result.
ZaidAlyafey said:Use that power series
$$\frac{1}{1-z} = \sum_{k=0}^{\infty}z^k \,\,\,\,\,\,\, |z|<1$$