Find the complex conjugate of the complex number \(z = 3\cos\theta + 3i\sin\theta\) where \(\theta = \frac{\pi}{6}\).

Step 1 ：Step 1: Replace \(\theta\) with \(\frac{\pi}{6}\) in \(z\), we get \(z = 3\cos\frac{\pi}{6} + 3i\sin\frac{\pi}{6} = \frac{3\sqrt{3}}{2} + \frac{3i}{2}\)

Step 2 ：Step 2: The complex conjugate of a complex number \(z = a + bi\) is given by \(\bar{z} = a - bi\).

Step 3 ：Step 3: Applying this to our complex number, we get \(\bar{z} = \frac{3\sqrt{3}}{2} - \frac{3i}{2}\)