Consider the function . Denote the punctured unit disc by . Let and . Which of the following statements is false?

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Consider the function <br><img src='https://www.fatskills.com/images2/GradExams/DB21F921-1D01-4B33-9730-344902E815B9.png' height='25' width='80'/>. Denote the punctured unit disc by <br><img src='https://www.fatskills.com/images2/GradExams/CC0DF283-AEAE-48B0-8221-44F6BDFF85B3.png' height='20' width='251'/>. Let <br><img src='https://www.fatskills.com/images2/GradExams/8CC392E6-69B8-4F62-B8F0-C6082DA272EC.png' height='15' width='42'/> and <br><img src='https://www.fatskills.com/images2/GradExams/834D5951-DFC5-496D-90D5-CD8BD8A70C65.png' height='15' width='45'/>. Which of the following statements is false?