Find complex number $K=\frac{\sqrt{1+z^2} + iz}{z - i\sqrt{1+z^2}}$

Question

Can anybody help me with the answer of this question?
$$K=\frac{\sqrt{1+z^2} + iz}{z - i\sqrt{1+z^2}}$$

Answer 1

Hint:

$$-i(\sqrt{1+z^2}+iz)=z - i\sqrt{1+z^2}$$

Answer 2

Hint: Multiplying numerator and denominator by $$z+i\sqrt{z^2+1}$$ this gives $$\frac{z\sqrt{1+z^2}+iz^2+i\sqrt{1+z^2}-z\sqrt{1+z^2}}{z^2+1+z^2}$$