Question # 03 (@) %23 Let I fa+bi; a,bEZli]:3 divides both a deal of the aring ZLi] of Gaussian integers. Solution and b. Prove that I is a mar

Q: Prove that (1+i)" +1(1-i)" = 2 cos %3D

A: We will solve the following

Q: Question 9: Given that z = cos+ i sin and u- iv = (1+z)(1 − j²z²). Show that 30 2 V = utan r = 4²…

A: For any queries please let me know through comments. I will try to reply ASAP! Please like if…

Q: using De-Moivre's theorem prove that cos π/7, cos 3π/7 and cos 5π/7 are the roots of 8x3-4x2-4x+1=0.…

A: The given equation 8x3-4x2-4x+1=0 Roots of the equation are cosπ7, cos3π7, cos5π7 use trigonometric…

Q: True or False The set of all solutions of the equation tan 0 = 1 is given by {o0 = + ka, k is any…

A: To find the solution of tan θ = 1 => (sin θ)/(cos θ) = 1 => sin θ = cos θ This is possible…

Q: 7- The indicated power for (1+ i)20 by using De Moivre's Theorem is

A: Given: 1+i20 we compare, 1+i=x+iy we get, ⇒x=1 &y=1 Therefore, r=x2+y2r=1+1=2r=2

Q: Prove : (1 - cos E)(1 + cos €)(1 + cot²0) = 1 %3D

A:

Q: 2п 2п 3. Find the fourth roots of 16 [cos(3 Hisin(). 3

A: Solution:-

Q: a) Find the square root 14+ 4√6. b) If ƒ(r) = (2+1), show that ƒ(r) — ƒ(r+1) = r(r+1}(r+2). Hence,…

A: B. f(r) - f(r+1)

Q: IF 2 = +i Sin I) UgE DE MOIVRES THEOREM TO fiND ALL CUBE Roors of 2.

A:

Q: [3(cos 18° + i sin 18°). [2(cos 20° + i sin 20°)]³.

A: De Moivre's Theorem: cosθ+isinθn=cosnθ+isinnθ where n∈ℤ

Q: Define   Degree 4; zeros: i, 1 + i

A: For a polynomial if a complex number z is a zero then its complex conjugate is also a zero. That is,…

Q: Find all exact solutions of cos(5x/9) = -1/2 show work

A: To find all the solutions for x

Q: Prove that: 1. Z, Z2 =r,r2[cos(8, + 02) + i sin(8, + 02)] 2.4=(cos(0, -62) + i sin(0, – 0,)] %3D 3.…

A: Here we use exponential form to represent complex Numbers.

Q: 2.2 Find upper bound of 2+4 (: - 3i)3 +1 where C is the circle |: – 3i| = 4.

A:

Q: 1 1. Prove the identity cosh2 r = 1 cosh 2x 2

A: As per our guidelines we are supposed to answer only one question at a time.  Kindly repost other…

Q: 5. [10] Use DeMoivre's Theorem to expand [4(cos 60° +i sin 60°)]". Write your answer in a + bi form.…

A:

Q: Find all solutions of tan(3√x−5)=1 where k ∈ Z. (Notation: k ∈ Z simply means that k can by any…

A: Given:

Q: Evaluate

A: To evaluate cosπ4+2π3, use the cosine addition formula, cos(a+b)=cos a cos b-sin a sin b and obtain…

Q: Which of the following correctly expresses 2sin(2β)cos(4β) as a sum?

A: Question is solved.

Q: Find the exact value of cos 0- if the termin side of 0- in standard position contains (6,-8)

A:

Q: Solve the problem from class: y'=y^(1/3) with y(0) = 0. How many solutions are there? How does that…

A:

Q: Express 9[cos(60°) - isin(60°)] in the form a + bi

A:

Q: 4 81-72sin²0+16sin*6 do S sin 20 de 1–2cos²0+cos40

A: Let…

Q: Find all solutions to cos(80) – cos(20) = sin(50) on 0 <0 < 3 0 = 0, Give your answers as a list…

A:

Q: O Find all sixth roots of z = 64 (cos 120° + i sin 120°). Leave your answer in Trigonometric Form

A:

Q: 1. State and prove the full version of the Pythagorean Theorem

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: Find all solutions to cos(7ø) – cos(4) sin(4ø) on 0 < ¢ < 3 Give your answers as a list separated by…

A: cos(7ϕ)-cos(ϕ)=sin(4ϕ)-2sin7ϕ+ϕ2sin7ϕ-ϕ2=sin(4ϕ)-2sin(4ϕ)sin(3ϕ)=sin(4ϕ)sin(4ϕ)+2sin(4ϕ)sin(3ϕ)=0sin…

Q: if z1= 3(cospi/12 + isinpi/2) z2= 2(cos7pi/12 + isin7pi/2) what is z1/z2?

A:

Q: Find the three cube roots of 8(cos 264° +j sin 264") and state which of them is the principal cube…

A: Given - 8cos 264° + jsin 264° To find - Find the three cube roots of 8cos 264° + jsin 264° and state…

Q: 3.16. Show that 10 (1 – i)49 (cos + i sin ) (8i – 8/3)6 - V2. -

A:

Q: (a) Is it true that cos (2 - 30°) = 2 cos 30°? Give exact answers in simplest form. (b) Expand cos…

A:

Q: Question 1 Suppose ZA ZD and AB= DE. What else is needed to prove AABC = ADEF by ASA? What else is…

A: GIVEN ∠A≅∠D and AB ≅DE

Q: Using de Moivre's theorem to compute (−1−√3i)^11 we find that the answer is?

A: For any complex number x and any integer n, r ( cos ⁡ θ + i sin ⁡ θ )n = rn (cos ⁡ ( n θ ) + i sin ⁡…

Q: Find the four fourth roots of z = 81 ( cos 4pi/3 + isin 4pi/3 ). write each root in standard form

A:

Q: Find all solutions to cos(5ø) – cos(4) = sin(3ø) on 0 < ¢ < T $ = Give your answers as a list…

A: To find the all solutions for the given trigonometric equation.

Q: tane – cot0 a. Prove 1 – 2cos?0 6. Show 1– 8sin?0· cos²0 = cos(40) | tane + cot0

A:

Q: Suppose a cell is suspended in a solution cor

A: Suppose a cell is suspended in a solution containing a solute of constant concentration Cs. Suppose…

Q: tane – cot0 a. Prove 1- 2cos?0 6. Show 1 – 8sin20 · cos²0 = cos(40) %3D 5. tane + cot0

A: To prove the given identities.

Q: QUESTION 2 Ustng De Molure's Theorem, evaluate 12 3 -itl ard leave four angwer in the form Z=a+ ib

A: Topic:- complex number

Q: 5. Evaluate | 3 ( cos 45°+ isin 45°) using De Moivre's Theorem.

A:

Q: Prove that (1+i)" + 1(1- i)" = 2m/2*1 nt cos 4

A:

Q: 3] 7 (cos 꼭 +isin 꼭) 4 V9 (cos 플,isin 끝) 5] Compute -3A +5B +2A

A:

Q: Find the three cube roots r1, r2 and r3 of 8(cos 264° + j sin 264°). Express all arguments in…

A: We have to find out cube root of unity for given complex number.

Q: Factor 11 + 3i in Z[i] into indecomposable Gaussian integers. Hint: use the norm to guess factors.

A: Using the norm to guess the factors.

Q: Find Bo aual Bi For BLUE

A: We know that the simple linear regression model is   y = (Beta)0 + (Beta)1x + e.

Q: Express 6(cos 2pi/3 + i sin 2pi/3) in the form of a +bi

A: Here the given polar form of a complex number is 6(cos2π3+isin2π3) . Now we express the polar form…

Q: 34) find the Maclaurin senes for fC2)= Cos 32

A:

Q: 3.37 Prove: So" sin" (x) dæ - + 0 as n → oo. (Hint: Use Theorem 3.3.1, but be sure to prove the…

A: Prove that ∫0π4sinnx dx→0 as n→∞. Let fn be the the function defined as fnx=sinnx. The sine function…