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 October 9th, 2018, 01:41 AM #1 Senior Member   Joined: Jul 2013 From: United Kingdom Posts: 471 Thanks: 40 2 Transformation Questions: Further Complex Numbers I need help with a couple of questions which can be found in Edexcel's AS and A Level Modular Mathematics FP2. Here it goes... 16. A transformation from the z-plane to the w-plane is defined by: $\displaystyle w=\frac { az+b }{ z+c }$, where a, b and c are elements of real numbers. Given that w=1 when z=0 and that w=3-2i when z=2+3i, a) Find the values of a, b and c, b) Find the exact values of the two points in the complex plane which remain invariant under the transformation. *I'm having particular problems with question b. October 9th, 2018, 02:52 AM #2 Global Moderator   Joined: Dec 2006 Posts: 20,965 Thanks: 2214 As w = 1 when z = 0, b = c. As 3 - 2i = (a(2 + 3i) + b)/(b + 2 + 3i), 3b + 12 - (2b - 5)i = 2a + b + 3ai. Hence 3b + 12 = 2a + b and 2b - 5 = -3a. Solving those equations gives a = 17/5 and b = -13/5. The invariant points are the roots of the equation z = (az + b)/(z + c), which is equivalent to a quadratic equation. Solving it gives z = 3 ± 4√(2/5). Thanks from perfect_world October 9th, 2018, 03:03 AM #3 Senior Member   Joined: Jul 2013 From: United Kingdom Posts: 471 Thanks: 40 For the second question, why does w suddenly become z? What's the purpose of this? May sound like a silly question - but I'd like to know. October 9th, 2018, 03:28 AM #4 Global Moderator   Joined: Dec 2006 Posts: 20,965 Thanks: 2214 As the transformation is from the z-plane to the w-plane, the phrase "invariant under the transformation" means that w = z. Thanks from perfect_world Tags complex, numbers, questions, transformation Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post chopnhack Algebra 2 March 21st, 2017 06:08 PM jonas Complex Analysis 2 October 13th, 2014 03:03 PM swtdelicaterose Linear Algebra 1 November 26th, 2009 04:06 AM envision Algebra 3 October 14th, 2009 06:04 PM envision Applied Math 1 December 31st, 1969 04:00 PM

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