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Question: \(\int_{0}^{50}{\lbrack\arg|z - 1|\rbrack dx}\), where \| \| is modulus and [ ] is greatest integer ...

∫050[arg⁡∣z−1∣]dx\int_{0}^{50}{\lbrack\arg|z - 1|\rbrack dx}, where | | is modulus and [ ] is greatest integer function is

A

0

B

25

C

50

D

100

Answer

0

Explanation

Solution

|z –1| is a positive real number

\ arg |z –1| = 0

\ ∫050[arg⁡∣z–1∣]dx\int_{0}^{50}{\lbrack\arg|z–1|\rbrack dx}= ∫0500dx=0\int_{0}^{50}{0dx = 0}