Question

Can anyone help with this complex number question?

Answer 1

I've done the first part, but I can't seem to do the second part using information from the first part.
The answer to the first part is:
\[z ^{5}-5z^{3}+10^{z}+1/z ^{5}+5/z ^{3}-10/z\]

Answer 2

the third term is just \(10z\)

(\(z\) is multiplied times 10, but \(z\) is not in the power of 10)

Answer 3

Right?

Answer 4

Yup, sorry. Typo.

Answer 5

z-1/z=2isin\(\theta\)

Answer 6

@behappy, I got the first part (which is what u got). But I don't know how it links to the second part .

Answer 7

Let

z =cos\(\theta\)+isin\(\theta\)
1/z = cos\(\theta-isin\theta\)

Answer 8

\[z^n=\cos(n\theta)+isin(n\theta)\\ 1/z^n = \cos(n\theta)-isin(n\theta)\]

Answer 9

now u may get the result