1.) Let G₁ = £1₁ 1₁ i -i) be group of 4 Complex numbers under mutiplication. a) is £1, i} a subgroup 6 // why? b.) is £1,1} a subgroup for and why?

Q: complex numbers then prove that If a, az, . . ..a, and b,, b, . .., b, are |a,5, + a,b, + ..+a̟ b̟²…

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Q: 17. Express 4xi + 5yi + 6xi? + 2yi“ in simplest a + bi form.

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Q: 1

A: If the n x n matrix obtained from the set is invertible then the set is a basis for Rn. In other…

Q: obtain 2- transform for the flow ing xCt) = tCt- 2T)

A: We have to use z transform table.

Q: show that the ring of complex umbers (+) Can be imbedding a ring of 2x2 matrics (M ₂x₂ 2X2

A: Given: A ring of complex numbers ℂ, +, · and a ring of 2×2 matrices M2×2, +, ·. To show: ℂ, +, · is…

Q: 6) Let R1 and R2 be relations on a set A such that R1 = {(1, 2), (2, 1), (3, 2), (3, 3)} R2 = {((1,…

A: Solution

Q: 1. Use Venn diagrams to exhibit A - (BnC)=(A – B)U (A – C). 2 Use memberchin tables to prove that4…

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Q: 6. (a) Use the Cauchy-Schwarz Inequality to prove that, for any finite sequences of complex numbers…

A: All the problems are application of Cauchy Schwarz inequality

Q: Consider the power Serics Ž n^ (x-z)^ n=1 Find the radins of conver genue shat is the intrvel of…

A: Consider the series ∑n=1∞nnx−2n We have to find the radius of convergence and interval of the…

Q: 7.) -2 (x-2)2

A: Topic = Limits

Q: 1 5) Verify the identity CSCX-1 + = 2tanxsecx cscx+1

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Q: 1) Determine the projection of a= [5, -4, 8] onto b = [3, 7, 6].

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Q: What is the range of the following function? 43 -2 7 5 4 3 2 1 & M T -5 a) {yÎR|y¹0} b) {yÎR} 1 2 d)…

A: Sol:- (1) Range of any function is represented by value on the Y-axis Correct option is (b)

Q: 51. Find U A¡ and A¡ if for every positive integer i, a) Aj = {-i, -i + 1, ., –1,0, 1, . , i – 1,…

A: 51) i be a positive integer so  i ∈ 1,2,3,4,......a) Ai =-i,-i+1,.....-1,0,1,.....,i-1,iA1 =-1,0.1 ,…

Q: 1. Specify the order of the zero z = 0 of the following functions: a) f(2) = z²(e* – 1), b) f(2) =…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Question 4 Note that if (j, k) and (m, n) are pairs of integers then we can add them in a natural…

A: A vertex set is the set of all vertices of the graph. There are two points in the  vertex set which…

Q: Let Prove - Order G be a that -1 a true of Is it equal to group the order that order and of the of D…

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Q: 1- The distance between two complex numbers z1 Z2 is denoted by: a) Iz – z2| b) /x + y c) Vz, + z2…

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Q: / Let 21, 22, ... a sequence of complex numbers such that Zn → z as n → ∞. Show that zn → ž. In…

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Q: Describe a sequence of transformations can be used to map AJKL onto APQR? K

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Q: Let f and g be permutations. Show that the order of h=fgf^−1 is the same as the order of g.

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Q: Check the associativity f binary dpatian 10ciatinity y binary qpeuatian, e3ubtraction and Division()…

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Q: PROVE THE STATEMENT "There exists a, b ∈ Z+, such that if a > 1 and b > 1, then gcd(a, b) > gcd(a^3,…

A: Given statement is wrong because there is no a, b ∈ Z+, such that if a > 1 and b > 1, then…

Q: 15) Prove that the groyp of complex numbers.under addinan is isomarphic to RR.

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Q: 12 2.345 -123456 -13 2.42 3). List the numbers in the picture above from greatest to least. Please…

A: Given: Numbers, 12, -13, 2.345, 2.42, -123456

Q: ve that the Bessel functionm generating funchion ie too

A: The aim is to show that∑n=-∞∞Jn(x)tn=ex2t-1t The approach for this proof is, Take,…

Q: Let a be a complex number with |a| < 1. Prove that <1_ iff |z|<1. z - a az

A: The given problem is to prove the following complex expression iff |z|&lt;1. To prove ,…

Q: Usually what is Ho in a one way chi square?

A: The one way chi-square test is also known as chi-square goodness of fit test. It is used to compare…

Q: 6) is {[a], [b], [c],[ b, c]} Complex? Explain your answer. on abstract simplice

A: 6) No, {[a], [b], [c], [b, c]} is not an abstract simplicial complex because it violates the closure…

Q: 10 Simplify (1+iv3)"

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Q: Subgroup of a sets of lefL is b) suppose thkat a Group G and and A,B are the right coseets of H in G…

A: Given: H is a subgroup of a group G and A, B are set of left and right cosets of H in G. To show:…

Q: proving card{Q} = card(QU{e,pi,sqrt(2)}) and also if A1,A2,A3 .... is countable, then The infinate…

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Q: 5. Evaluate lim 3x5-4x²+1 x-00-7x5+x²+2 a) co g 8 MIN 3 c) Does not exist 3 d)

A: To evaluate the given limit of function

Q: What is the domain of the graph above? O A) [-2, 0) Ов [-5, — 2)U (-1, o) C) [-2, 3] O D) [-5, – 2)…

A: Solution

Q: 4. In the ficld (C,+, ) of complex numbers, define the mapping f: C- C by the rule f(a, b) - (a,…

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