Express $z = \dfrac{3i}{\sqrt{2-i}} +1$ in the form $a + bi$, where $a, b \in\Bbb R$. 
Express $$z = \frac{3i}{\sqrt{2-i}} +1$$ in the form $a + bi$, where $a, b \in\Bbb R$.

I figure for this one I multiply by the conjugate of $\sqrt{2 +1}$? But I’m still struggle to achieve the form $a+bi$.

Given $$\dfrac{3i}{\sqrt{2-i}}+1=\dfrac{3i+\sqrt{2-i}}{\sqrt{2-i}}$$
Now $$=\dfrac{3i+\sqrt{2-i}}{\sqrt{2-i}}\times \dfrac{\sqrt{2+i}}{\sqrt{2+i}}$$$$=\dfrac{3i\sqrt{2+i}+\sqrt{5}}{\sqrt{5}}$$
$$=\dfrac{3i\sqrt{2+i}}{\sqrt{5}}+\dfrac{\sqrt{5}}{\sqrt{5}}$$ 
