3. Given $i$ is the imaginary unit, then in the expansion of $(\sqrt{3}+i)^{10}$, the sum of all odd terms is
512 .
Analysis It is known that the sum of all odd terms in the expansion of $(\sqrt{3}+i)^{10}$ is the real part of the complex number.
Also,
$$
(\sqrt{3}+i)^{10}=\left[(-2 i)\left(-\frac{1}{2}+\frac{\sqrt{3}}{2} i\right)\right]^{10}=(-2 i)^{10}\left(-\frac{1}{2}+\frac{\sqrt{3}}{2} i\right)^{10}=(-1024)\left(-\frac{1}{2}+\frac{\sqrt{3}}{2} i\right)=512-512 \sqrt{3} i
$$

Therefore, the required result is 512 .