Complex numbers, expressed in the form a + bi, extend the concept of real numbers by incorporating the imaginary unit i = √(-1). While their introduction often seems purely theoretical, complex values have widespread applications in science, engineering, and technology. They are fundamental in electrical engineering (AC circuit analysis, impedance, signal processing), fluid dynamics, quantum mechanics, control theory, electromagnetism, and even finance and computer graphics. Complex values provide elegant solutions to problems involving oscillations, waves, stability, and optimization that cannot be easily addressed using real numbers alone. Exploring their real-life applications helps bridge the gap between abstract mathematics and practical innovation, highlighting how complex values model systems that are multidimensional, periodic, or inherently unstable.