Converting an expression: from angular frequency to Laplace variable $\ s =j \omega$

Question

I have the expression:

$$Z=\frac{A}{\sqrt{\omega}}+\frac{A}{j\sqrt{\omega}}$$

$$Z=A \sqrt{\frac{j}{s}}+\frac{A}{j}\sqrt{\frac{j}{s}}$$

I'm trying to get an expression with s variable, but it is very difficult. Can someone help me please?

If in the expression there are both s and j (e.g. $ 1+js$), is it right?

Thank you in advance.

Answer 1

Hint: substitute $$\omega=\dfrac{s}{j}$$can you finish now?