Question

Team Task 7: Complex number as matrices MATHS 120 Wednesda y, May 22, 2019 In this team task, you will investigate how complex numbers can be represented trices with real entries, in such a way that multiplication of complex numbers corresponds to matrix multiplication. as 2 x2 ma a -b. For example, For a, b e R and : a+ bi e C, let M, be the 2 x 2 matrix a Problem 1: What is M-1 Problem 2: What is Mi? Note: M-1 and M, are 2 x 2 matrices and therefore each corresponds to a linear transf mation from R2 to R2 Problem 3: Describe the linear transformation corresponding to M-1 geometrically Problem 4: Describe the linear transformation corresponding to Mi geometrically. Problem 5: What is (M)2? Let w = a + bi and z = c + d, with a, b, c, d E R. Problem 6: Check that MuM,M Bonus Problem: How does Problem 6 shed light on Problem 5? Conclusion: We have seen how to represent complex numbers as 2 x 2 matrices w efficients. Moreover, as shown in Problem 6, the multiplicative structure of complex n completely encapsulated by the matrices. (One can show that the additive structure

Answer 1

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