Let $(a\_n),(b\_n)\subset\mathbb{C}$, be two sequences of $\mathbb{C}$ such that 
$$\lim\_{n\longrightarrow +\infty}|a\_n|^2+|b\_n|^2=|\lambda\_1|^2+|\lambda\_2|^2.$$

Is it true that
$$\lim\_{n\longrightarrow +\infty}a\_n=\lambda\_1,\;\;\displaystyle\lim\_{n\longrightarrow +\infty}b\_n=\lambda\_2??$$
Thank you.