(b) Let z = x + iy = re?". Find |z| and z² first in terms of x and y and then in terms of r and 0. Under what circumstances does |z| = z2?

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A: Rationalise  all the term and calculate to get the final answer.   Actually as per the barteleby…

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A: Here, the given equation is: x2d2ydx2=2y...(1) To show that ϕ(x)=x2-x-1 is the solution of (1) on…

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A: We have to prove given identity: Concept:

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Q: Q53- X--) (xij-Xi - X.j+X)=Zero 13D 「に )に prove that e to

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A: Introduction: Wronskian of a given set of functions is very useful to examine whether the functions…

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A: We need to prove that the solutions of the equation: cosh(z)=1 are z=i2kπ, where z∈ℂ, k∈ℤ.

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A: The given information is: Xi~U0, θ or fx=1θ,   0&lt;x&lt;θ The null and alternative hypotheses are:…

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A: Given that             fz=z4-5z2      and    C=z∈ℂ : z=1.

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A: use partial differentiation for finding the derivative.

Q: -2 Let f(t,y) = y + 3t?e'. Then f satisfies a Lipschitz condition in y with L = 2, given that 1<t<2.…

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Q: show that Ф (x, y, z) = аф PDE : агф дуг + дуг I х2 +у2 +Z2 024 072 satisfies the

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Q: 4. Use the I.V.T and Rolle's Theorem/M.V.T to prove that the equation below has a unique solution in…

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Q: 1° = 2 + 3+ 4 + J6. 2 Prove cot 7- %3D

A: Use the properties of trigonometry to prove this

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Q: Given DE Cauchy-Euler xy +2y In x, x>0 what is the particular solution?? II. -In x+x I x II. IV.…

A: Given that : x2y' + 2y = ln x

Q: 2) al X,X2 =) y = Xi~ ? ,-,Xn ~lid exporen tíal ( 100 b) Xq, X2,--- Xn~ iid N(44i44)= ビ- ~? i=1 %3D…

A: Solution : a) Given : xi  ~ exp ( 44100 )   ; i = 1,2,3,...,n ∴ θ = 0.44     Y    = ∑1n Xi It is…

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Q: 4. Let z = x2 + y³, x = 2st, y = s - t2, s = u", and t = u sin w. Compute for Oz ду and дw ди

A: Let z=x2+y3, x=2st, y=s-t2, s=uw, and t=u sin w.To compute for ∂z∂w and ∂y∂u.

Q: 27. Show that कक्या 1 Vn E Z*. T1\2i+1 2i+2. i=0 (2n + 2)!'

A: Consider the given expression. ∏i=0n12i+1·12i+1=12n+2! Consider the left side of the equation.…

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A: Since you have asked for a multiple question, we will solve the first question for you. If you want…

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A: Given  yh = C1*eat + C2ebt

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A: To prove: ∫r2-x2dx=x2r2-x2+r22sin-1xr+C

Q: Proue that || A|1maπi <j <n 1 Σajl . m

A: In the given question we have to prove that   A1 = max1≤j≤n{∑i=1maij}                         (1)the…

Q: ) Fnl the Vdume of the Selid enclesed by the curres "about the x-axS. y=e^, y=0 x =©,'x=/

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Q: dv Prove that 4u/2n

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Q: 2. Give the condition which ensure that |ez| < 1 where z in C.

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Q: I. Solve using De Moivre's Theorem. Given that z is not real number and z = 1, show that w = z-1 z+1

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Q: Which of the following is a general solution to the followin x²y"+xy'+ (x²– 1)y=0 y=c,(x) +cY_,(x) O…

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