Discussion
Where does \( w = z^{2} \) fail to be conformal?
Answer: C
The derivative is \( 2z \), which vanishes only at the origin. There the map doubles angles rather than preserving them: a right angle between the axes becomes a straight angle, since \( \arg w = 2\arg z \). Such a point is called critical, and conformality is lost exactly where the derivative is zero
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