Complex numbers extend real numbers by including the imaginary unit i ( \( {i}^2=-1\Longrightarrow i=\sqrt{-1} \) ). Written as a + bi, they have a real part (a) and an imaginary part (b). They are essential in mathematics and engineering for solving equations (like x2 + 1 = 0) and analyzing systems such as AC circuits. This chapter provides a comprehensive exploration of complex numbers.