Question

If \( f(z) \) is analytic at \( z_0 \), then it is

• A. Continuous everywhere
• B. Discontinuous everywhere
• C. Continuous at \( z = z_0 \)
• D. Discontinuous at \( z = z_0 \)

Hint:

Analyticity at a point guarantees continuity at that point.

Answer 1

The Correct Option is C

If a complex function \( f(z) \) is analytic at a point \( z_0 \), then it must be differentiable in some neighborhood of \( z_0 \). Differentiability implies continuity, hence \( f(z) \) is continuous at \( z_0 \).