What Is a Conformal Map?

A conformal map is a function that preserves angles locally. That means, tiny shapes are not squished or stretched in weird ways, but their angles stay the same.

Why Are Conformal Maps Important?

They are used to transform complicated regions into simpler ones, making problems easier to solve—especially in physics and engineering.

Examples of Conformal Maps

• The function \( f(z) = z^2 \) doubles angles at every point (except the origin).
• The function \( f(z) = \frac{1}{z} \) inverts the complex plane.

Applications

Conformal mappings are used in fluid dynamics, electromagnetism, and even cartography (map-making) to preserve local geometry.

Key Points

• Conformal maps keep angles intact.
• They’re powerful tools for transforming and simplifying problems.