Mathematics · Complex Analysis
For any complex-valued function f, let Df denote the set of points on which f satisfies the Cauchy-Riemann equations. For which of the following functions is Df equal to the entire complex plane &mathbb;C?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1f(z) = z / (1 + |z|)
- 2f(z) = (cos αx - sin αy) + i(sin αx + cos αy), where z = x + iy and α = 0✓
- 3f(z) = e-1/z4 if z ≠ 0, and f(z) = 0 if z = 0
- 4f(z) = x2 + iy2, where z = x + iy
Correct answer
f(z) = (cos αx - sin αy) + i(sin αx + cos αy), where z = x + iy and α = 0
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