Let 2=x+iy be a complex number such that coshz 0. Then Im(tanhz) is equal to * sinhycoshy sinh²x+cos²y the above: sinycosy sinh?x+cos²y the above

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Q: Q4:B/Simplify [cos 40+ i sin40 1³ [cos 20-i sin2015 using De Moivre's theorem?

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Q: Find the product of zı and z2 Given zı = 4 (cos 180 ° + i sin 180 °) and Z2 = 4 (cos 145° + i sin…

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Q: Do the functions y, = cos4t and y, = sin4t constitute a fundamer %3D The functions constitute a…

A: The given differential equation is y''+4y=0 the auxiliary equation is D2+4=0 D2=-4D=±2i therefore…

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A: For multiplication of complex numbers the angles add.…

Q: 3- Represent in the form of x+ iy a) V8 (cos + i sin m) b) 6 (cos 7 + i sin7)

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Q: (a) Buktikan, Prove that, (sin x + cos x)* = sin" 2x + 2 sin 2x + 1. %3D

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: Express z 14/2(cos135 + isin 135) to it rectangular form.

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Q: Let 2=x+iy be a complex number such that coshz#0. Then Re(tanhz) is equal to * sinhycoshy…

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Q: Find the points of intersection between r2 =2 cos20 and r=- %3D 1- cose

A: Find the points of intersection between r2=2cos2θ and r=21-cosθ. for the intersection points both…

Q: let 2=x+iy be a complex number soch that coshe hen Im(tanhe) is equal to sinhycoshy sinh?x+cos²y

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Q: Find the product of z1 = 2 (cos 213° + i sin 213 °) and Z2 = 4 (cos 33 ° + i sin 33 °) %3D

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Q: z = 2ev Ве ev-sinx – 3e*÷cosv) find: www a2z a2z az a)- дудх ,b). дхду 4 ax

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Q: Prove using the IVT. tan-1x = cos-1x has a solution.

A: Given :                      tan-1 x = cos-1 xSolve :                     tan-1 x = cos-1 x…

Q: (4) Prove the formula cosh x - sinh2 x 1 using the methods in this workshop. In other words, express…

A: Consider the given identity

Q: Let z1 = r1(cos θ1 + i sin θ1) and z2 = r2(cos θ2 + i sin θ2) be complex numbers, then the…

A: Given that, z1=r1cosθ1+isinθ1z2=r2cosθ2+isinθ2

Q: how that cos 1+cos 8 and sin 1-Cos 0 %3D %3D using de Moivre's Theorem.

A: It is required to show that cosθ2=1+cosθ2 and sinθ2=1-cosθ2 by using de Moivre's theorem. By de…

Q: 2c. Show that * (5 - ) 4 sin z - cos 2r + 3 -8 cos for every r.

A: To prove: 4sinx-cos2x+3 = 8cos4π4-x2 We know that cosx-y  = cosxcosy+sinxsiny and cos2x= 1-2sin2x

Q: a) By using convolution theorem, show that 1 (sin 3t – 3t cos 3t). 54 1 L-1 (s² + 9)2

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Q: cos (3z) + sin(3z) c: |2| = 2 to be -dz: Calculate the integral value. 23 (Complex functions theory)

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Q: solve for allvalues of x in the interval 0 ≤x≤2π:  2-2sin^2 x+3 cosx=-1

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Q: Find all the roots, of 2=+1+V3j A =D/2 (cos +j sin-) - B z=V2 (cos (-+ka) +j sin ( + ka)), k=-1,0…

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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: Let z=x+iy be a complex number such that coshz #0. Then Re(tanhz) is equal to

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Q: What is r 1- O Option 1 2 2 sin 0-3 cos 0 3 y = ² x + 1 2 x² + y² = 2y²-3x Option 3 in Cartesian…

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Q: Prove that i2-i0 e-e %3D sincd

A: We have to prove eiθ-e-iθsin θ=2i Now, sin x can be expressed in exponential form as sin…

Q: sin(2r) cos(2x) +1 2. Prove: csc(2x) + cot(2r). %3D COS

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Q: 9-10.j Show that sin20 2tane %3D 1+tan20

A: We will prove the trigonometric formula.

Q: Calculate ∫9sin^4(x)cos^2(x)dx

A: Given: ∫ 9 sin4 x cos2 x dxFormula: cos2 x = 1-sin2 x…

Q: ered # tion Bi Q) choose one only 1. If (x + y)² = x² + y² prove that = - dx 2. If y = sin³ () cos³…

A: To find the differentiation of given functions.

Q: Let z=x+iy be a complex number such that coshz#0. Then Im(tanhz) is equal to

A: None of these is correct.

Q: Find a series of cosines of multiples of x which will represent (x sinx ) in the interval (O, x) and…

A: Let's expand x cos(x ) , xcosx=x1-x22!+x44!-x66!+...=x-x32!+x54!-x76!+...             in 0,x To show…

Q: dr 5) J, (2z– 1)3/2 (2x – 1)3/2 4 cos( sin2( dr

A: Integration is the process of finding the anti-derivative function of the given function.…

Q: Let z=x+iy be a complex number such that coshz#0. Then Im(tanhz) is equal to sinxcosx sinh²x+cos²y…

A: Formule: 1. 2sinhAcoshB = sinh(A+B)+sinh(A-B)   2coshAcoshB = cosh(A+B)+cosh(A-B) 2. Sinh(iz) = i…

Q: (a-B) (at sin (a+B) 2- show that cosa – cosß = -2sin 2.

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Q: Find the points of intersection between r 2 = 2 cos20 and r =- %3D 1- cose

A: We have to find the intersection between r2=2cos2θ and r=21-cosθ.

Q: 3. sin(2x - 6) = cos(4x + 18) %3D

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Q: 4. Express in the form a + jb, (i) 2(cos 30° +j sin 30°) (ii) 5(cos 57° -j sin 57°)

A: To write in the form of a+jb

Q: Find the points of intersection between r =2 cos20 andr=- %3D 1- cose

A: To find the intersection point two curve we have to find r,θ by solving given curve.

Q: 3. у %3D tan1(sinh 2x) Зсosh-1 (csc) 4. у %3 CSC

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Q: cost+cos4t+cos7t / sint+sin4t+sin7t = cot4t

A: SOLUTION-

Q: z1 = 30 (cos 20° +i sin 20°) and z2 = 6 (cos 5° + i sin 5") %3D %3D ( cos +i sin %3D

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Q: 2 Find the points of intersection between r=2 cos20 and r = 1- cose

A: given r2=2 cos 2θ and r=21-cosθwe need to find the intersection between two polar curves

Q: 9. Use the Residues Theorem to calculate 1+ sin² ª -de. Sketch the contour you used.

A: We have to find integral using Residue Theorem.

Q: Find all roots of cos a- a2 - x = 0 to five décimal places.

A: In order to find roots of this equation, we plot graphs of x2+x and cos x. Intersection points of…