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

Q: ſcos 3t sin 8t dt * 1/2 (-1/5 cos5t - 1/11 cos11t ) + C O 1/2 (1/5 cos5t - 1/11 cos11t) + C O None…

A:

Q: Peter purchased a cottage for $360,000. He paid $32,500 down and agreed to make equal payments at…

A: Solution-The price of the cottage =$360000Down payment=$32500Rate(r)=3.2% or 0.032Time(t)=8…

Q: What is the EXACT value of COS (5) 6 ?

A:

Q: 3i +2V2 - 5n -4i +6(1 +a T/4 [(3sec2 t)i - (5 + sin t)j - (6sec t tan t)k)]dt Find 0. 2 2-57T-4 3i +…

A: ∫sex2xdx =tanx+c∫(constant)dx=x+c∫sint dt =-cost +c∫sect tant dt =sect+c tanπ4=1cosπ4=12secπ4=2

Q: 10. Using Cauchy's Residue Theorem, evaluate -2π (cos 30)² 1-2p cos 20+p² d0,0 < p < 1.

A:

Q: Evaluate cos[arcsin ( -) + arccos 1. (10 + 13 v3)/26 O (12 + 5V3)/26 (12 + 5V5)/26

A: Ģiven, cos(arcsin(-1/2)+ arccos(5/13))

Q: Let 1, Z₁, Z2, Z3, ..., Z-1 be the nth roots of unity. Then prove that (1-z₁)(1-z₂) ... (1-Zn-1) =…

A:

Q: (d) (27+5)(2- i)|=/3 12z +5|. %3D

A: Solution D: We have to prove (2z¯+5)(2-i)=3(2z+5) L.H.S. Let z=x+iy So z¯=x-iy therefore…

Q: 7. Evaluate * (D5 - 3D4 + 8D³ + 16D² - 9D - 13)y = 0 y = (C₁ + C₂x)e¯x + С3ex +C4e²x cos3x + C5e²x…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: 1+sece cos0+1 1-sece cos0–1

A:

Q: The th roots ofz=a+ bi whenk=0, 1, ..., n-1. take the form: 0+2n COS 0+2n +i sin O [cos(0+ 2kx) +i…

A:

Q: = -2 + 11i, z2 = 2 – i. Showing the details of %3| | your work, find, in the form x + iy: Re (z).…

A:

Q: 7)Use Taylor theorem to estimate cos(0.23) with Jerror|< 10-2

A: Here we are to estimate cosx at x=0.23=23100 with error≤10-2,using Taylor theorem i.e, using Taylor…

Q: 3. There are three distinct cube roots of any nonzero real number c. (a) Set up an algebraic…

A: Sol:- (a) To find the three distinct cube roots of a nonzero real number c, we can set up the…

Q: The complex exponential Fourier series coefficients a1 and a_1 of x(t) = cos(2nt)u(t) are O a1 = 2…

A: Consider the given signal x(t)=cos(2πt)u(t)

Q: H-W/ Prove that the Ah root of (-1) are a, ew, awim a w* Since a= cos CF) +i Sin () W= COS (2 )a i…

A: We know that  e^(ix) = cos(x) + i sin(x)  ( cos(x) + i sin(x) )^n = cos(nx) + i sin(nx)

Q: 10. Subtract 2- V- 64x²y* from – 3– xy-9y' and express the result in a + bi form

A: Answer and explanation is given below

Q: prove that theta(2m) = theta(m) when m is odd and theta(2m) = 2 theta(m) when m is even

A: We can start by using the definition of theta notation to prove these statements. Recall that theta…

Q: Find how much interest $25,000 earns in 4 years in a certificate of deposit paying 9.5% interest…

A:

Q: Let. a 3 = (-) = -(1) - P = ( ) 5 and a) Find Fourier Coefficient of b with respect to a . b) Find…

A:

Q: Find the root (3 – 3i)2 - + V18[cos(r/8) + isin(x/8)] O +V18[cos(x/8) – isin(t/8)] +3 V2[cos(1/4) –…

A:

Q: The function (f) with a period of 2π is defined by: f(x) = cosh (x - 2π)  if x∈[π ; 3π] a)…

A:

Q: Find the equation in red in the same way as the equation in the second picture(I need same by…

A:

Q: The square root of (1 2i) is (1) V5 (cos (+ 2n)+ i sin (5 + 2n")) for n = 0,1 COS (2) V5 (cos (+ 2)…

A: The general form of a complex number is given by z=a+ib, where a,b are two real numbers and i=-1.…

Q: : Find Fourie trans form? alt)= 5 rect(134) @ F[214-2) +²0+] e @ F[x(++) cos(3+)] Sext] © F[z(t)…

A: “Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: Prove that 3 12 56 -1 -+ cos 5 sin sin 13 65

A: