The word "繁忙" is formed by combining the character "繁", meaning numerous or complex, with "忙", meaning busy. "繁" incorporates the component "糸" (thread) to suggest intricacy, while "忙" uses "忄" (heart/mind) and "亡" (perish) to imply a preoccupied state. Their semantic meanings merge to denote a busy condition marked by multiple or complicated tasks.