Mechanical Engineering > GATE 2026 > Complex Variables
If w = logez = loge(x + iy), where i = √−1, then which one of the following statements is correct?
A
w is analytic everywhere except at z = 0
B
w is non-analytic everywhere
C
The conjugate functions of w are loge(x2 + y2) and loge(x2 − y2)
D
The conjugate functions of w are tan−1(x/y) and tan−1(y/x)

Correct : a

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