Let z=x+iy be a complex number such that coshz#0. Then Re(tanhz) is equal to * sinhxcoshx sinh²x+cos?y O the above O None of these sinxcosx sinhycoshy sinh?x+cos?y sinh?x+cos?y O the above: O the above: sinycosy sinh2x+cos²y

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

A: According to our company policy we can only answer first question and rest of questions can be…

Q: a. Z1 Z2 = r1 r2 [cos(0, + 02) + j sin(0, + 02)] %3D Z1 =" [cos(0, - 02) +j sin(01 – 02)] b. | | Z2…

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Q: Find the product z;z2 and the quotient 1. Express your answers in polar form. z2 cos()- + i sin), z2…

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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: b) Find the inverse ztransform of the following: i z's zl2|sin 3 2(2/2/cos 3)z+|2/F] zz(z*+4z+1) 1…

A: We will use the basic knowledge of the theory of z-transforms to answer all the three subparts of…

Q: 11. An expression that is equivalent to 2tan z Otan z Ocot z 02 cot z sin 2x 1-cos 2z is

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

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Q: Let z1 = 2(cos() + i sin 12 and z2 = 6(cos() + i sin). Find z1z2 and (Enter your answers in a + bi…

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

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Q: The cos'ydy is equal to 3 A. siny + sin?y +sin³y - sin'y+ C sin'y + C 3 1 B. siny – sin³y + siny -;…

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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: 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: Determine c1 and c2 so that y(x) = c1 sin 2x + c2 cos 2x + 1will satisfy the conditions y(?/8)= 0…

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Q: The auxiliary roots of the auxiliary equation associated with a certain HLDE are m=±3, ±3i, + 3i.…

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Q: (b) Show that U (x, y) = eu cos v, V(x, y) = eusin v are conjugate harmonic of each other if f = u +…

A: It is given that,  f = u+iv  is analytic. We have to show that,  U(x, y) = eu cos v  and  V(x, y) =…

Q: III) Prove: 2) cos x x + sin æ sin y = sin 3y (3) COS (2) for all x and y such that x+y= 2

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Q: Show that (cos x + isin x)n= cos nx + isin nx whenever n is a positive integer. (Here i is the…

A: We can prove given result by mathematical induction: Define a statement p(n).  Show that p(n) is…

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: 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: de B: Evaluate the 2m a-cos20 when z = et and Iz| = 1. %3D

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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: 1 ,3 -r/a0 ? 0 ,² dr sin0d0 ø do = x 32na cos X = ? 0 Jo Jo

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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: If the integration by parts was used to integrate the product of e^ax and sin(bx) and cos(bx).…

A: 1. To evaluate the integral ∫eaxcosbxdx+i∫eaxsinbxdx:

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: Consider J sin'x cos²x dx. If we let "=cos x , the integrand can be transformed to. A 2u2 - - | (u²-…

A: The given integral,     ∫sin5x cos2x dx

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: to the I. sinx(e+ 1)x' - cosx = 1, y(=) = 0 %3D %3D (1 + e) (1 + cos x) = 0 (1 + e) (1 + sin x) = 2…

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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 simplified rectangular form of 9 cos r+j9 sin- 24 cos 짜124 sin + v6cos ㅠ+ jvV6 sin 금ㅠ+…

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Q: r(cos0+isin 0) with 0 (exact) in (0°,360°): а. z = 12-12i Z, =-3-3i z, =-4V3+ 4i b. с. Z3 = %3D

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Q: The cos'ydy is equal to 3 1 A. siny + sin³y + sin³y -; sin'y + C 5 3 B. siny – sin³y +sinsy -sin?y +…

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Q: • Find a harmonic conjugate of u(r, y) = x² – 2x – y². Show that u(r, y) = e" cos y is harmonic.

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Q: Prove that (a) Pn (cos 0) = 2F1(-n,n+ 1; 1; sin²0/2).

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Q: Determine c1 and c2 so that y(x) = c1 sin 2x + c2 cos 2x + 1 will satisfy the conditions y(pi/8) = 0…

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Q: Find the area. a. Inside one leaf of the three-leaved rose = cos30 b. Shared by the circle r=2 and…

A: Given that a) r=cos(3theta) b) r=2 and r= 2 (1 +sin(theta)) c) r=-3cos and r=1-cos( theta) We have…

Q: b. Determine real (e/z) in terms of x and y. C. Use Euler's formula to prove that expression; = cos…

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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: (1) Given that z = 1-iV3, express z in the form r(cos e + i sin e) Hence write down z7 the form

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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 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…