1. **State the problem:** Given the complex number $u=2(\cos(\frac{\pi}{5})+i\sin(\frac{\pi}{5}))$, express it in exponential form and understand its meaning. 2. **Formula used:** Euler's formula states that $e^{i\theta} = \cos\theta + i\sin\theta$. 3. **Apply Euler's formula:** We can rewrite $u$ as: $$u = 2e^{i\frac{\pi}{5}}$$ 4. **Explanation:** This means the complex number $u$ has magnitude (modulus) 2 and argument (angle) $\frac{\pi}{5}$ radians. 5. **Summary:** The given expression $2(\cos(\frac{\pi}{5})+i\sin(\frac{\pi}{5}))$ is exactly equal to $2e^{i\frac{\pi}{5}}$ by Euler's formula. **Final answer:** $$u = 2e^{i\frac{\pi}{5}}$$