Responsive Website Header Development

I need a simple, responsive website header section built using HTML and CSS.

Requirements:
- Fixed top navigation bar with logo and menu (Home, About, Contact)
- Gradient background
- Mobile responsive design with dropdown menu
- Additional elements: search bar, social media icons, call-to-action button
- Clean and modern layout
- Completed within 1–2 days

Ideal skills and experience:
- Proficiency in HTML and CSS
- Experience with responsive web design
- Strong eye for modern design aesthetics
- Ability to meet tight deadlines

Please include examples of previous work.