Analytic function with image in an affine real line Created 2026-09-24 Updated 2026-09-24
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If is a holomorphic function on a connected domain and
(1)
then the Cauchy-Riemann equations force both components of to vanish. Hence is constant.
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Past exam of the mathematics course of the University of Cambridge / 2002 / ib / Paper 2 / 7B / Solution Created 2026-09-24 Updated 2026-09-24
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Past exam of the mathematics course of the University of Cambridge / 2002 / iii / Paper 16 / 5 / Solution 2026-10-03
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Past exam of the mathematics course of the University of Cambridge / 2002 / iii / Paper 31 / 5 / Solution 2026-10-03
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Past exam of the mathematics course of the University of Cambridge / 2002 / iii / Paper 5 / 4 / Solution 2026-10-03
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Past exam of the mathematics course of the University of Cambridge / 2003 / ib / Paper 1 / 7B / Solution Created 2026-09-24 Updated 2026-09-24
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Past exam of the mathematics course of the University of Cambridge / 2003 / iii / Paper 70 / 4 / b / Solution 2026-10-03
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Past exam of the mathematics course of the University of Cambridge / 2003 / iii / Paper 9 / 1 / b / Solution 2026-10-03
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Past exam of the mathematics course of the University of Cambridge / 2004 / ib / Paper 2 / 5A / Solution Created 2026-09-24 Updated 2026-09-24
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Past exam of the mathematics course of the University of Cambridge / 2004 / iii / Paper 9 / 4 / ii / Solution 2026-10-03
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Past exam of the mathematics course of the University of Cambridge / 2004 / iii / Paper 9 / 4 / i / Solution 2026-10-03
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Past exam of the mathematics course of the University of Cambridge / 2005 / ib / Paper 3 / 5F / Solution Created 2026-09-24 Updated 2026-09-24
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Past exam of the mathematics course of the University of Cambridge / 2005 / ii / Paper 4 / 24H / ii / Solution Created 2026-09-24 Updated 2026-09-24
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Past exam of the mathematics course of the University of Cambridge / 2006 / ib / Paper 1 / 3D / Solution Created 2026-09-24 Updated 2026-09-24
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Past exam of the mathematics course of the University of Cambridge / 2006 / iii / Paper 54 / 3 / Solution 2026-10-03
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Past exam of the mathematics course of the University of Cambridge / 2007 / ib / Paper 3 / 5F / Solution Created 2026-09-24 Updated 2026-09-24
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Past exam of the mathematics course of the University of Cambridge / 2008 / ib / Paper 1 / 3C / b / Solution Created 2026-09-24 Updated 2026-09-24
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Past exam of the mathematics course of the University of Cambridge / 2008 / iii / Paper 53 / 2 / Solution 2026-10-03
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