<s>[INST] 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 $a+bi$.
 [/INST] $\displaystyle z=\frac{3i}{\sqrt{2}-i+1}$
$\displaystyle =\frac{3i}{\sqrt{2}-i+1}\times\frac{\sqrt{2}+i+1}{\sqrt{2}+i+1}$
$\displaystyle =\frac{-3+(3+\sqrt{2})i}{(\sqrt{2}+1)^2+1}$
$\displaystyle =\frac{-3+(3+\sqrt{2})i}{4+2\sqrt{2}}$
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