Use the formula of Theorem 11.7 to demonstrate that we can be at least (1 - a) 100% confident that the error we make is less than e when we use a sample pro- portion Ô Χ = - n with as an estimate of 0. α/2 n = 4e2 Zα/2 Ô (1–0) n

Q: 483 2.

A: Given: 12+32i483

Q: 1. Prove Euler's formula: Let z e C (the set of all Complex numbers). Then: eiz = cos z +i sin z

A:

Q: 1. Prove that the set of complex numbers, together with complex number addition and multiplication…

A:

Q: |=1|+ |= 2 | |- |- | 3. If z3 + z,, show that VI +

A:

Q: Given the following complex numbers:    A = 3-2j  ,  B = 12+3j  ,  C = -5+7j  ,  D = -3-5j Use…

A: We are given the following complex numbers, A=3-2jB=12+3jC=-5+7jD=-3-5j We have to find the value of…

Q: (a) Prove the validity of the following expression: N-1 { N, 1-aN 1-a' a = 1 a" for any complex…

A: Here we use simple property of Gromeric series ans it's convergence criteria .

Q: 2. If a and b are complex numbers, and z is a complex number that obeys |z| = 1, show that az + b =…

A: Given that a,b and z all are complex numbers.   let, a=c+idb=r+is  and z=x+iy, where c,d,r,s,x,y all…

Q: Consider the squaring iterations of complex numbers where the fixed point is zero. Without…

A: We need to find whether the starting points yield a bounded or unbounded iteration.

Q: he length of any edge of a regular tetrahedron (a tetrahedron whose edges are equal in length is…

A:

Q: Question 10 : Find all values of k for which A is diago- nalizable, given that A

A: For the solution of the problem follow the next step.

Q: 1. Find the cube roots of −1+√3i then represent each root in the argand plane

A:

Q: 2. Relationship between neutral geometry and incidence geometry. (a) Explain how the axioms stated…

A: note :As per the instructions we will only solve part (2) of the question.In neutral geometry, there…

Q: (k) (zw)-1 = w-!z-1

A:

Q: 1. If z = 1+ iy is a complex number. Find the principal argument and exponential form of z =

A: Given that z=x+iy is a complex number. where, Real Part = x and Imaginary Part= y Now,  z=i1+i…

Q: Question 1: | E a,b: * s E la.|² E l6:1?.† i=1 For the above inequality ai, bi, 1 < i<n are complex…

A: It is required to prove that, ∑i=1naibi2≤∑i=1nai2∑i=1nbi2. Prove by induction as follows: For n=1:…

Q: QUESTION 3 Given real numbers x and y with x < y, prove that there is a rational number q such that…

A:

Q: et z=a+bi be a complex number such that hat: - |z +i| = 5 -2т Arg(z – 3) 3 Consider the following…

A:

Q: Given the complex numbers z = 9+7 i and w = -9 – 9 i, calculate: i) 3 z = ii) w2 iii) 3 z – 2 w =…

A:

Q: 11. The vertices of an equilateral triangle are equidistant from the origin. One of its vertices is…

A:

Q: |2| = (x² + y²)'/2

A:

Q: Given the complex number z = (1 - ai/2 - i) - (b - 2i/1 + 3i), where a and b are real. If arg z3 =…

A:

Q: 1. Consider the set S inside the complex plane. S is the set of all points z such that |z| < 1.…

A: We will determine boundary condition for set S and then defined all required sets

Q: Given the following complex numbers:    A = 7-2j  ,  B = 1+5j  ,  C = -4+6j  ,  D = -7-j Use your…

A: Given: The given complex numbers A=7-2j , B=1+5j , C=-4+6j, D=-7-j

Q: the expression (oualtivalued ) Find all values of

A:

Q: Show the 2 points that satisfy the equation in the complex pione. i) | 2 - 11 = 2.12 +1|

A:

Q: .The set of complex numbers is an ordered set 0 صواب İhi O

A:

Q: Could you do a formal proof of the following: (you may rely on Theorem 4.6.1, that is irrational).…

A: