English: An example of Joukowsky transform of a circle into an airfoil. The circle in complex plane is centered at (-0.08,0.08) and has a radius of 1.08.
The above figure is the complex variable ${\displaystyle \zeta =\chi +i\eta }$ such that ${\displaystyle \left|\zeta \right|={\sqrt {(\chi +0.08)^{2}+(\eta -0.08)^{2}}}=1.08}$ and the transformed variable below is another complex variable ${\displaystyle z=\zeta +{\frac {1}{\zeta }}=x+iy}$.