Any continuous group homomorphism from $\mathbb{R}$ to $GL(n,\mathbb{C})$

Question

Any continuous group homomorphism $\phi$ from $\mathbb{R}$ to $GL(n,\mathbb{C})$ is of the form $\phi (t)=exp(tX)$ for some $X\in M(n,\mathbb{C})$. Can anyone give hints for the proof of this fact? I consider the case $n=1$. But I cannot see why $\phi(\mathbb{R})$ must be on the unit circle. Thanks!