The phrase "a complex responsibility" is correct and usable in written English.
You can use it when describing a duty or obligation that involves multiple factors or challenges.
Example: "Managing a large team comes with a complex responsibility that requires strong leadership skills and effective communication."
Alternatives: "a multifaceted duty" or "a challenging obligation."
In a Huffington Post blog she wrote, Leading today is an incredibly complex responsibility and it can easily become so busy and overscheduled that leaders find themselves lacking in the very skills we most need them to have, the very skills that mindfulness can strengthen -- focus, clarity, creativity and compassion.
However, scaling up the global pharmacy workforce is a complex, multifactorial responsibility that requires coordinated action.
"There are more expectations now being put on school boards, and with more complex responsibilities comes a greater demand on their time," she said.
By performing these tasks dynamically, a designer is relieved from complex responsibilities such as task allocation and synchronization.
The Department for Work and Pensions is a huge department with many very complex responsibilities.
Prominent among 'personal' issues in this study and elsewhere [ 6, 35], are the demands and complex responsibilities associated with an extended primary carer role outside of work - contributing to a desire to work less hours.
The S.B.A., in response, said that writing the rules was a "complex and controversial responsibility" to establish guidelines to set-aside contracts based on gender.
The office of executor or administrator may involve complex responsibilities.
Focus is especially important when faced with complex responsibilities, multiple tasks, deadlines, and uncertain outcomes.
The latest crisis between Israelis and Palestinians is more complex than the obvious American errors in Iraq and Afghanistan, with roots in ancient enmities and complex responsibilities going back to the Holocaust and beyond.
