Prove that e²1+²2 e²1e²2 for all 21, 22 € C. Hint: The function ƒ(z) = e²eª-≈ has ƒ' (z) = 0 for any fixed complex number a € C. Use arguments from functions of one variable to show that f is constant (=eª) on C. Show that Show that = cos²z + sin² z = 1, for all z e C. sin(2₁ +22) = sin(z₁) cos(z2) + sin(z2) cos(z₁), for all 2₁, 22 € C.

Q: Problem 2 For vectors A = (-1,–2,3) and B = (-1,3, –4), show that the relation ||A+ B||² – ||A –…

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Q: Express the function as a 11) trigonometric function of x. Must show ALL wor Cos 4x

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Q: u + (1+ сos u) = 0

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Q: Q4. Let fla) < cos" ( a ) Find fCa) COS n+5 f'(a) = %3D

A: Answer is mentioned below

Q: 14. Prove that (1- cos x) csc x = 1

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Q: J32 For z = cos(x-4y) show that # дудхду 332 дугах

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Q: find the possible values of (x) for each of the following # 1) y = cos T+X 4 1+ 4 (use Domain…

A: Sine function is denoted as y=sinx The domian of the function is -∞,∞ and the range of the function…

Q: Consider the following difference equation: fk k = 0, 1, 2, · . . 1+ fk' fk+1 = with fo is…

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Q: SOLVE STEP BY STEP IN DIGITAL FORMAT ●コヅシッシ 2*@*!??!!??! ¿¡ !?! Wa - XXX O * Take Aeikx+ Be-ikx &♪…

A: To Show: Aeikx+ Be-ikx = C cos(kx)+ D sin (kx) Now, cos(kx) = (eikx+ e-ikx)/2 sin(kx) = (eikx-…

Q: 3. ox (- w) and ¢x (@) are complex functions, i.e., x (- w) = ¢x (w)

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Q: 3. Compute : exp(sin m(e÷)).

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Q: Express 1+ cos a + i sin a in the modulus amplitude form.

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Q: lim, o (cos z)= takes which indeterminate form? А. 100 В. 00 С. оо D. Е. 1 х о 8 -18

A: Here, we can solve it by taking the limit of individual terms.

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

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Q: 73. Derive cos (u + v) = cosucos v – sinusinv by using the identity for cos (u – v) and the odd and…

A: Our Aim is to derive cos (u+v)=cos(u) cos (v)-sin (u) sin (v)-(i) by using the identity for cos…

Q: Convert r = √2 cos(-) to cartesian.

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Q: 4. Evaluate tan (4.3 – j1.1).

A: Given that, evaluate tan (4.3 - j1.1).

Q: (A+B)* = A† + B*, (AB)† = B* A*, (AA)† = XA*, %3D %3D where A is a complex number and AŤ indicates…

A: We have to evaluate ABC†. Given AB†=B†A† Hence, ABC†=ABC†=C†AB†USe AB†=B†A†=C†B†A†=C†B†A†

Q: z is a complex variable z=x+iy pic attached with question  Evaluate using L’Hospital’s rule

A: To calculate the limit of the given indeterminate form using L'Hosptial rule

Q: 18. Solve 2 tan r-1 0 over [0, 27).

A: Unlike the sine and cosine functions, the tangent function is π periodic. That is, if the point (x,…

Q: 4. Evaluate these complex numbers: (a) (40/50° + 20/-30°)¹/2

A: Since you have asked multiple questions, we can solve first question for you. If you want other…

Q: Prove that the distance of the roots of the equation sin 0₁ 2³ + sin 0₂2² + sin 031 z + sin 041 = 3…

A: Given equation is  |sinθ1|z3+|sinθ2|z2+|sinθ3|z+|sinθ4|=3 Prove That : The distance of the roots of…

Q: дz дz Let z = sinh(7x + 8y). Find and ax ду дz ax дz ду || 7 cos(7x + 8y) 8 cos(7x + 8y) х х

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Q: √ (3(1 + cos 0))² + (−3 sin 0)² do

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Q: #6. Eunlwate taldx uhere cosk fa) cosx-SinZx, x)n .

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Q: w=tan inverse[ ((1-z)/(1+z)) ] is a complex function, what is the mapping conformal  of unit circle…

A: We will find the first seethe image of (1-z)/(1+z) when IzI=1

Q: 5. +y=ye-² (ve-²) ³ Ans: - e* = ce³x

A: Let us solve the given Ordinary Differential Equation in the next steps.

Q: Q/ Evaluate the following functions 1.In(3-16) 3. cos ¹ (1+i 3) 2 (3|0.52) 2. e ‚4. tanh¯¹ (2-i5)

A: According to the given data, evaluate the functions:

Q: Madaurin f(x) = cos(7)

A: Find the Maclaurin expansion of  f(t)= cost

Q: Prove that sin? 0 – sin* 0 = cos? 0 – cos* 0. cos“ 0.

A: We can use the trigonometric identity, sin2θ+cos2θ=1 sin2θ=1-cos2θ.

Q: Q1 // Choose the correct answer for the following :- 1- L(e"sinh*t) = a);G-→ »G *9G- 2-L(12cos2t) =…

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