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

Q: Find the indicated power using De Moivre's Theorem. (Express your fully simplified answer in the…

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Q: 2. If z = cos 0 + i sin 0 where 0 is real, show that 1 1 - i tan- = - 1+z 2z 1-z2 Express: а) 1+z2…

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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: B- If x+= = 2 cos Ø prove that x"+ 2 cos rø by used complex number.

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Q: The intersection points between the curves r = 3. and r = are 1-cos e 1+cose

A: The given curves are, r=11-cosθ                      ........(1) r=31+cosθ…

Q: Express the number -5 in the form R(cos(0) + i sin(0)) = Reil where R>0 and 0 <0 < 2T.

A: rewrite -5 as -5=-5+0i comparing with z=a+bi a=-5 , b=0 R=a2+b2=-52+02=25+0=25=5 now…

Q: Find all angles between 0 and 2n satisfying the condition V2 COS T = Separate your answers with…

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Q: Find the product z₁z₂ and the quotient Z1Z2 = N 11 Express your answers in polar form. Z2 Z₁ =…

A: We know that general property of trigonometry is - Cos(A+B ) = CosACosB - SinASinB. And Sin(A+B) =…

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: Show that sin mx cos nx dx = 0 for positive integers m and n: i using the primitive, ii using…

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Q: Find the indicated power using De Moivre's Theorem. (Express your fully simplified answer in the…

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Q: Prove that: 2n 1 cos=0 + i sin 0) + 10 2cosne - %3D eino

A: If  is an exponential form of a complex number where x and y are real numbers then its polar form…

Q: z is a complex variable, z=x+iy question attached as photo

A: To verify the values of the two  given definite integrals

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: Find all angles between 0 and 2T satisfying the condition COS X = 2 Separate your answers with…

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Q: 27 de Evaluate the intergal using the residue theorem. 12 + 6 sin e

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

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Q: Evaluate the principal 5th root of z = 50 (cos150° + j sin150°) and find the absolute value (r).

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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 cubic root of z = V27 + 3i in the form of r cis 0. 1 (Hint: tan =

A: Given:- Z=√27+3i To find:-  Cubic root of given complex number

Q: Find the product z,z2 and the quotient 4. Express your answers in polar form. Z2 z1 = V3 (cos(55°) +…

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

A: according to bartleby guideline, I can solve first question...

Q: التاريخ اليوم موضوع الدرس A) Discuss the conrergence of facx) %3D on A = Co,0)

A: Convergence of the sequence

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: Show that COS x dx a² – x² sin a 2а where a is some positive number.

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Q: cos z = cos x cosh y– jsin x sinh y

A: Complex numbers

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

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Q: 27 do Evaluate the intergal using the residue theorem. 0, 15 + 3 sin 0

A: The given problem is to evaluate the given integral using residue theorem, we have to convert the…

Q: B- If x+! += 2 cos prove that x"+= 2 cos rø by used complex number.

A: we have to show that the following

Q: ) Let Z= re q iy be a complex mumber Such that cosh Z+o. then Re (tanh z) is equal to Sin a cesn

A: In the given question we have to find the real part of tanhz and and also check it that is it equal…

Q: Let r(t) (sin(4t), cos(41), sin(4f) cos(81)). Find the point where r(t) intersects the xy-plane on…

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Q: Evaluate the complex integral e19.1.png rx+yi dz az + b if a = 2, b = 6, c= 17, x = 1, and y = 6.…

A: Given  a= 2 ,b=6 ,c= 17  x= 1 and y=6 x+iy= 1+6i

Q: do Evaluate the intergal using the residue theorem. 12 +1 cos 0

A: ∫02πdθ12+1 cosθLet, z=eiθ . Then cosθ=(z+z-1)/2, dz=iz dθ, so that∫02πdθ12+1…

Q: The complex integral J(tan 2rz) dz is,

A: Introduction :

Q: Show that r = cos(2pi) is symmetric about the y-axis.

A: The solution of the problem is given in the next step.

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: 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: 2 de Evaluate the intergal using the residue theorem. 12 + 6 sin 0

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Q: Verify that the Cauchy-Riemann equations are satisfied for the following functions. Where z is a…

A: To verify the Cauchy -Riemann equations for the given analytic functions f(z)

Q: Let f(z) : D → C be a complex function. Is it possible for both f(z) and f(z) to be analytic? • If…

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Q: Evaluate the complex integral e19.2.png rx+yi | Vaz + b dz if a = 2, b = 14, c = 16, x = 2, and y =…

A: The given problem is to evaluate and simplify the given complex integral with unknown variables…

Q: Evaluate the secondary 5th root of z = 50 (cos150° + j sin150°) and simplify to rectangular form O…

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Q: Evaluate the complex integral mq3.1.png •x+yi | asinh(bz) dz if a = 7.4, b = 3,v = 5, x = 3 and y =…

A: The given problem is to evaluate the given complex integral with unknown variables values and also…

Q: 27 de Evaluate the intergal using the residue theorem. 13 +4 sin 0

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Q: Prove that: Z,Z2 =r,r2[cos(0, + 02) + i sin(0, + 02)] 1.

A: NOTE- As we are allowed to answer one question in one session so, i have answered first one for you.…

Q: Prove by MSE that a. sin 90° = 1 b. cos 180° = -1

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

A: first option is correct answer. Thankyou

Q: Find the indicated power using De Moivre's Theorem. (Express your fully simplified answer in the…

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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…