22. The complex numbers wi and w2 have modulus 1, and arguments ai and a2 respectively, where 0< a1 < a2 < Show that Arg (w1 -w2)= (a1+a2-T). T 2

Q: 4. Let z = -4 + 3i and zw = -7 – 2i. By showing clear steps, find w in the form of a+bi.

A:

Q: 1) Prove that there are no positive integer solutions to the equation x2-y?=1

A:

Q: Find the two smallest positive solutions of 5sin(5x)=3

A: 5sin(5x)=3 sin(5x)=.6 sin(5x)=sin36.87°

Q: Prove that Eo 2i = 2n+1 – 1 - i3D0

A:

Q: 17. Given a = 4 – 4i and az = 4 + 3i, express %3D :11 in the form a + bi. a, az CLONE Dec 19

A:

Q: =[12] and U- = -[] Then A2017U is equal to -1 Let A =

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Q: 86. Show that Z, = r(cose + isine) and Z2 = r[cos(-6) + isin(-6)] are conjugates. %3!

A: Given,

Q: 4. Let z = -4 + 3i and zw = -7– 2i. By showing clear steps, find w in the form of a+bi.

A:

Q: We assign a complex number Am to each n-tuple of non-negative integers m = (m₁, ..., mn)…

A:

Q: Vhich among thế chôičes satist etters only. 2а. у" - Зу'- 10у %3D0 Co-5x C o2x

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Q: 1 Show that 2-* d.x 2 In 2

A: We can show the answer in the following steps.

Q: Prove using the IVT. For all positive integers k, cos x = xk has a solution.

A: Intermediate value theorem: Let f be a function continuous on a closed interval a,b. Let k be number…

Q: 10- Solve the problem: Utt-4uxx = xt, 00 u(x,0) = x, 4(x,0) = 0, u(0, t) = 0, Ux(1,t) = 1+t, t20 %3D

A: Given, utt-4uxx=xt;   0&lt;x&lt;1, t&gt;0 ⋯⋯⋯⋯1ux,0=x,   utx,0=0,   0≤x≤1,⋯⋯2u0,t=0,   ux1,t=1+t,…

Q: We consider the Complex numbers x,y, z with modulus 1 with the property that: x + y + z = 0 and the…

A: Trigonometry is a branch of mathematics that studies relationships between side lengths and angles…

Q: 1-Show that У +їх ave X + iy =/=1 where Complex numbers ? X+iy and

A:

Q: 2.3 Use the Cauchy integral formulae to evaluate 22 - 1 Jo (9 – 2*)(2 + 2i))" where C is a circle |2…

A:

Q: Suppose z=a+bi , w=u+vi, a=((|w|+u)/2)^(1/2) , and b=((|w|-u)/2)^(1/2) . Prove z^2=w if v≥ 0 and…

A: Given z=a+bi,w=u+iv,a=w+u212,b=w-u212. Need to show that z2=w if v≥0, and z2=w if v≤0.

Q: 4) For A = ajax + azāy + azaz , B = b,ax + b2ay + bzaz, show that A.B cos 0 = A.AVB.B

A:

Q: (9) Is an complex annullus Ann(2o, R1, R2) with 0 < R1 < R2 simple connected?

A: Note: As per bartleby instruction when more then one question is given only one has to be answered.…

Q: 3V Show that there dã do not exist two real numnbers which add to 7 and multiply to 13. It is not…

A: our objective is to conclude the result

Q: 8. Work out a Gaussian quadrature formula of the form Ans. A; = 1, x; = Aif(x1) + Arf (x2). f(x) dr

A: The given problem is to prove the following integral, the proof is to show the 2 point gaussian…

Q: i) Find an upper bound for the modulus 3z³ + 5z + 1, if |z|<1 where z is the complex number.

A: Now for the mod function: : a+b≤a+b. SO using the same method in the given complex function:…

Q: [1E q14] Question is attached, Thanks ?

A: From the given information it is needed to prove that:

Q: (2) Suppose that G, C Zn-r. Then prove that G,-1C Zn-r+1

A: We prove that

Q: Theorem 9 Let {um}=-5 be a solution to Eq. (18) and suppose that u-s = a, u-4 = b, u_3 = c, u_2 = d,…

A: We are asked to show the following equation, u8n-3=c2ne2n∏i=12nic+a∏i=12n-1ie+c Using the identity,…

Q: Question # 03 (@) %23 Let I fa+bi; a,bEZli]:3 divides both a deal of the aring ZLi] of Gaussian…

A:

Q: Theorem = 7 K 51 M 25

A:

Q: 1- Find the and argumint g fallowing modulus the Complea numbers 2+i 2+ i 3-i 4i + (Hi)?

A: It is given that

Q: 1. If z = x + iy is a complex number. (a) Verify that v2|z| > |Re(z)| + |Im(2)| [Hint: Reduce this…

A:

Q: Theorem 9.If k is even and I, ở are odd positivVe integers, then Eq.(1) has prime period two…

A: Given, if k is even and l, σ are odd positive integers.

Q: 3 If C is a circle of radius r with centre z, in the complex z-plane and if n is a non-zero integer…

A: Consider the given integral as, ∮dzz-z0n+1

Q: (i) find gcd(2,3+5i) in Z[i], (ii) show that 3+4i and 4-3i are associates in Z[i] , do all , dont…

A: Solution (i)

Q: (d) Determine the right cosets of ((1 2), [1]) € S3 x Z2.

A: I just used the definition  of cosets

Q: Theorem 4.8.1 Irrationality of V2 V2 is irrational.

A: For any integer n such that n² is even then n is also even.

Q: (Chapter 3.2. Ex.# 49) Show that if fi(x) is O(g1 (x)), f2(x) is O(92(r)), and f2(r) # 0 and g2(r) #…

A: Given: If f1x is ⊝g1x, f2x is ⊝g2x, and f2x≠0 and g2x≠0 for all real numbers x&gt;0.

Q: Question is attached, Thankyou

A: Let us take z = x + iy.

Q: 3 If A = 1] show that A² - 5A + 7I = 0. %3D %3D -1 2

A:

Q: Use DeMoivre's Theorem to find the following. Write your answer in standard form. V2 cis- 20 O…

A: Given (√2cos(9π/20))5

Q: 4. Let z = -4 + 3i and zw = -7 – 2i. By showing clear steps, find w in the form of %3D a+bi.

A:

Q: As you know, given z e C, z + 0, then z1/2 is a set containing two distinct elements, so that the…

A:

Q: 2+13 Evaluate zdz along the following paths- (a) horizontally from 1 +i2 to 2+ i2 then vertically to…

A:

Q: A (real or complex) scalar u is said to be an nth rootof unity if un = 1. Let ωn = e 2πi n . Use…

A:

Q: 12) a-:]- B-[:: ind AR 3 0 3 -2 1 Find AB. %3D -2 1 0 4-3

A:

Q: Suppose that the complex number z has modulus one, and that 0 < Arg z < . Prove that 2 Arg(z+1) :…

A: Given the complex number z has modulus one, and 0&lt; Arg z &lt; π/2. So, we may take complex number…

Q: (Chapter 3.2. Ex.# 49) Show that if fi (x) is O(g1 (x)), f2(x) is O(g2(æ)), and f2(x) # 0 and g2(x)…

A:

Q: IRI- 2. <| sinz|< -e 2

A:

Q: Find the modulus and argument of (a) Z₁ = -√3+√ and (b) 2₂ = 4+ Y j Hence express Z₁ Z2 and 2₁/22 in…

A:

Q: For a Cauchy-Euler DE the roots of auxiliary are m = -3 + 3i then Ye = x= (c, cos(3 In x)+ c2 sin(3…

A:

Q: 2. Sketch 0 in standard position if cose = 8. and deter %3D

A: Given that: cosθ=-817

Q: (a)] Show that 1+(1+z)/2 csch z In • [(b)] Use part (a) to find all the values of csch (-2i).

A: Let:

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.