The point M(a, b) represents the complex number \( a + bi \) on the complex plane, where:
\[ a + bi = r(\cos \varphi + i \sin \varphi) \]
\[ [r(\cos \varphi + i \sin \varphi)]^n = r^n (\cos n\varphi + i \sin n\varphi) \]
\[ \tan \varphi = \frac{b}{a}, \quad \cos \varphi = \frac{a}{\sqrt{a^2 + b^2}}, \quad \sin \varphi = \frac{b}{\sqrt{a^2 + b^2}} \]
Complex numbers extend the idea of one-dimensional numbers to two dimensions. They help interpret mathematical and physical phenomena where direction and magnitude are involved.