30. The complex number 1 + V3i can be expressed in exponential form as 2e A в 2e- is 2e- 2e D

Q: 2π 6 11. 3r2 sin e drd0 0 0

A:

Q: .1 Determine the possible values of xif 2x|2|x-3|. Hence, give your answer in interval notation. 2…

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

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

Q: 28. The general solution of the equation tan(2x +) = It A.2x = nn - -B. 2x = nt +"C. 2x = nT + D. 2x…

A: According to the guideline we should have been able to solve only first question of the demanded…

Q: Give the general solution to у" — 4 у'+ 20 у 30 а) О у-С, сos(4 х) — С, sin(4 x) b) O y=C, e**+C, e…

A:

Q: Find all the exact solutions of 2cos^2x+2=5cos(x)

A: Consider the following equation:…

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

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

Q: If z = 2 ( cos 2¥/3 + isin 2¥/3 ), then z^3=   i. 2 - i8√3 ii. -4 + i4√3 iii.-8-i√2 iv. -8 - i4

A: Using de-moivre's formula :

Q: Number 1a

A: Given cubic equation is,

Q: Compute Re if z₁ = 5√√2 + 2√3i, and z2 = 3√√√2-5√3i 2

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Q: Find the general solution to 2 0 0 -10 1 -3 2 7 + 0 cos (2t). 0 2 -4

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Q: 11) (3ysos(3a By cos(3

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Q: 8- Evaluate a) ſe² + 4 sin(8z) dz 1+9cos(8z) бх- х2 b) J 73-9x²+8 esc²) dx Csc2 - х3-9х2+8

A: We have to use proper substitutions.

Q: 3. Show that (1+i) = 2i

A:

Q: What are all of the solutions for the equation 2sin?(0) + 3sin(6) + 1 = 0 on the interval of [0,…

A: We can make it easier for you.

Q: 2. The exact value of sec 57 is O2 2V3 -2 2V3 3

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Q: 3 of u(a,9) = Cof"( 4y Cof' (+y then provethat ace +4u + Sin2ce=0

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Q: 11. Show that 1 + 4i is a root of the equation 2z3 - 3z2 + 32z + 17 = 0. Hence, find all the roots…

A: Answer

Q: 12. Show that the equation z + iz + 1 = 0 has neither a real root nor a purely imaginary root.

A: Note: According to bartleby we have to answer only first question please upload the question…

Q: 12. Explain why the solutions of the simultaneous equations ax + by + c = 0 dx + ey + ƒ = 0 have…

A:

Q: Find all values of the complex function of z for the e^(3z)=1z=x+iy

A: Its given that e3z = 1.  Given, z=x+iyWe need to sovle for z.

Q: If A= B = verify that A(B + C) = AB+ AC. :) 1 If A = 2 and B show that (AB)" =B'AT 4 -1

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Q: 2) × if it was 2+4i and 2=3-1 3+1 2+i 2 prove that x² + 3xy + y² = 6 =

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Q: if (1+i)(x+iy) = 2+4i then 5x is : O 15 O 10 O 5 O 3

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Q: Express as a product.cos 5t + cos 6t

A: Given : cos 5t + cos 6t

Q: Show that in (5.2) the average values of sin mr sin nx and of cos mI cOs na, m+ n, are zero (over a…

A: Given problem is :

Q: у 3 Сі сos 2х + с2 sin 2x y = cqe2* + c2xe²2x

A: See the details solution in below

Q: 5. Find ALL degree solution of 3sin 0 + 3 = 2 cos' 0.

A:

Q: 8. The reason why cos²(x)-2=0, [-27,27] has no solution is because cos(x) is undefined for x =+ /2.…

A: Given that,  Cos^2(x) -2= 0 Cos^2(x) =2  Cos x= +-√2= +-(1.414)

Q: 5] compute: 7A -5B where: 2+3i itqi -si A = 3+7i -4 ?b-8 7 3ti 2+si ?5-8 5-2i -4-3i 8ミ チ+

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Q: Which of the following is a cubed root of (-/3 - 9? (A) 21°[cos(8z9) + i sin(8z9)] (B) 21[cos(7x/9)…

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Q: 7/4 *(1 – sin 2t)3/2 cos 2t dt

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

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Q: 5) Evaluate the real integral 27T 1 de (5+ 3 cos 0)(13+5 cos 0) by complex variable methods, i.e.,…

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

A:

Q: What are the steps to solve for θ in the equation 2sin⁡(θ)=0.651

A: We have to find theta

Q: 1. Lat A - [; : - and B = 2 2 1 3 4 (a) Compute AB. (b) Compute BA.

A:

Q: A (0, 8) В (4, -12) С (9, -1) D (-8, -8) Е (1,-3) F (3, 5) ULLV 1. Identify the component form of…

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Q: 1. Use the graph of y = VI to estimate the solution(s) to the following equations YA -150 -120 -90…

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Q: Solve for v. 3 v+5 -56=-14 If there is more than one solution, separate them with cor If there is no…

A: Solve the equation

Q: Which of the following representations of a quadratic has complex roots? Oal 9z2 + 33 = 0 y -2.5 -2…

A: For finding which quadratic equation have complex, we find roots of all equation given in options…

Q: 2/2 00 (-1)" (2n + 1)³' COs nx 1°) Show that dr = Justify your reasoning. n=1

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

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Q: 15. Show that the equation, 2³ + e* = 0 has exactly one real root.

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Q: 2. Solve: tan(3 T - 4) = 1 Te [0, 1 %3D 2 T = 80 %3D 10 3 A %3D 25 T = 20 %3D 3 л

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Q: 6. у %3D Gе" сos 3х + C,е* sin 3x

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Q: Solve: Subject to 2wt+3ux + 4u = 0 u (x,0) = x² in R. x [0,00)

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Q: -1 3 -6,Compute A-5I,. 9. Let A=-8 7 -4 1 8

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Q: Compute z -20 where z is the complex number 6(cos 70° + i sin 70°). (i) 6²º(cos 40° + i sin 40°) 1…

A: To compute z-20 where z is the complex number 6cos 70°+i sin 70°.

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.