Complex Numbers: Polar and Exponential Forms

This GeoGebra example visualizes the polar representation (modulus and argument) and exponential form (Euler's formula) of a complex number in the complex plane. It demonstrates how a complex number Z can be expressed as r(cosθ + i sinθ) or re^(iθ), highlighting the geometric meaning of modulus r and argument θ. The construction uses the Vector command to draw the position vector from origin to Z, Angle to mark the argument, Length to compute the modulus, and If to handle quadrant-correct angle display. Text objects text1 and text2 show the algebraic forms. Suitable for high school or introductory university students learning complex numbers, this interactive tool helps bridge algebraic and geometric interpretations and supports classroom demonstrations.