Problem - 2245
Let complex number $z_1=2-i\cos\theta$, $z_2=2-i\sin\theta$. Find the maximum value of $|z_1z_2|$.
$$|z_1z_2|=\sqrt{4+\cos^2\theta}\sqrt{4+\sin^2\theta}=\sqrt{20+\sin^2\theta\cos^2\theta}=\sqrt{20+\frac{1}{4}\sin^22\theta}\le\sqrt{\frac{81}{4}}=\boxed{\frac{9}{2}}$$