If z = r(cos 0 + i sin 0) is a complex number, then z" [cos( ) + i sin(

Q: Find the product of the two complex numbers. 21 = 3 (cos 10 +i sin 10") and zg=-2(cos 35" +i sin…

A: Given: x1=3(cos 10°+i sin10°) and x2=-2(cos 35°+i sin 35°)

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: Find the product in the complex plane. + i sin + i sin Cos

A: I

Q: Let z be a complex number. Then the solution(s) of sinhz+coshz=1/e is (are)

A: The posted question has multiple questions but according to guidelines we will solve the first…

Q: 3i

A: First we have to write in the polar form basis, z=r(cosθ+isinθ) Given : z=(4-5i)cos(1+3i) To…

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: What is the result of multiplication of complex numbers -V3+i and (cos + i sin )? 3

A: Let z_1 = - sqrt 3 + i = r cos theta + i . r sin theta r cos theta = - sqrt 3 r sin theta = 1 Then…

Q: 4. If the two complex numbers z1=ri(cos01+ i sin 01) and z2= r2(cos 02+ i sin 02) then the numbers…

A: The given complex numbers,z1=r1cosθ1+i sinθ1 and z2=r2cosθ2+i sinθ2

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: Determine all complex solutions of the equation cos(z) = 2.

A: First represent cosz in exponential form then make quadratic equations to find solutions as in next…

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A: A complex number can be written in the cartesian form a+bi and the equivalent polar form reiθ. Polar…

Q: Find the three unique cube roots wk of the complex number z = 8 (cos 48° + i sin 48°). Write exact…

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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: Express the complex number z = 4 – 4/3i in polar form r(cos 0 + i sin 0). Select the correct answer…

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Q: Find the quotient z1/z2 of the complex numbers z1 = 50(cos 4π/3 + i sin 4π/3) and z2 = 5(cos π/3 + i…

A: Find the quotient z1/z2 of the complex numbers .

Q: 5. Find the complex cube roots of 27 (cos 306° + i sin 306°)

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Q: Find all solutions to 2 cos(0) = - 1 on the interval 0 <0 < 2n %3D

A: Given that, 2cosθ = -1 and interval is, 0≤θ&lt;2π We have to find all solution in the given…

Q: 6. Find all complex cube roots of 27(cos 219° +i sin 219°).

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Q: Find the product of the complex numbers z1 = 4(cos 50° + i sin 50°) and z2 =  7(cos 100° + i sin…

A: Given complex numbers - z1 = 4cos50°+isin50°                ..........................(1)z2 =…

Q: Express the complex number z = -6/3 – 6i in polar form r(cos 0+ i sin 0). Provide your answer below:…

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

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Q: Express the complex number -3i in the form R(cos(0) + i sin(0)) = Ree where R> 0 and 0 ≤ 0 ≤ 2.…

A: The given complex number is -3i

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: Find the quotient z1/z2 of the complex numbers z1 = cos 70° + i sin 70° andz2 = cos 230° + i sin…

A: The two complex numbers are given as , z1=cos70°+isin70° z2=cos230°+isin230° The value of z1z2 can…

Q: Given the complex numbers  z = 8 (cos(8π/15) + i sin(8π/15))  w = 1/2 (cos(17π/15) + i…

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Q: Find the general solution of у" -у - бу %3D 6х3 + 26 sin 2x

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Q: Find the quotient z1/z2 of the complex numbers z1 = 3(cos 5π/18 + i sin 5π/ 18) and z2 = 10(cos π/16…

A: Given two complex numberz1 = 3cos5π18 + i sin5π18z2 = 10cosπ16 + i sinπ16

Q: Show that 2 cos(x) = 3x has exactly one real solution.

A: As we know that if the function is strictly increasing, f'(x)&gt;0 or strictly decreasing,…

Q: Consider the following complex number. z = 36(cos (210°) + i sin (210°)) (a) Find two square roots…

A: Using De-Moivre's theorem we get

Q: Use DeMoivre's Theorem to find the 5th power of the complex number z = 2(cos 24° + i sin 24°).…

A: Solution :  Given that  Z = 2 (cos 24° + i sin 24°)

Q: Express the given complex number in rectangular form (a + ib). T 1. + i sin + i sin cos 9. 9.

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Q: 2. Convert r = -8 cos 0 into Cartesian equation.

A: r2=x2+y2 x= r cos theta y= r sin theta

Q: What is the result of multiplication of complex numbers -V3 + i and (cos + i sin ) ? A)1(cos 뚫 +isin…

A: We have to multiply the given complex numbers . The solution is following

Q: (a) Express the complex number 2 + (2/3)i in the form r(cos 0 +i sin 0), -n < 0 <T. (b) Solve the…

A: Complex numbers are those numbers which is represented in the form of a + ib where is a real part…

Q: Consider the following complex number. Z = 4(cos (280°) + i sin (280°)) (a) Find two square roots…

A: Root of complex number

Q: What is the result of multiplication of complex numbers -V3 + i and (cos + i sin .)? 57

A: Given complex numbers are -3+i, 18cos5π3+isin5π3

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: The polar form of complex number (z=3+3i) is O 3 (cos 45+ i sin 45) √2 (cos 45 + i sin 45) O 31/2…

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Q: Let z be a complex number. Then the solution(s) of sinhz+coshz=1/e is (are) *

A: I have provided solution in step2.

Q: Find the four fourth roots of z= cos 4p/3 i+ sin 4p/3 . Leave your answers in trigonomet-ric form.

A: De Moivre's law: cosθ+isinθn=cos nθ+isin nθ.

Q: Convert the complex number 4(cos(30°) + j sin(30°)) = Z from trigonometric form to rectangular form.…

A: The trigonometric form for a complex number is : z=r(cos θ+ jsin θ) . The rectangular form for a…

Q: Express 6(cos 2pi/3 + i sin 2pi/3) in the form of a +bi

A: Here the given polar form of a complex number is 6(cos2π3+isin2π3) . Now we express the polar form…

Q: Solve the following complex numbers 1. sin[ln(8 + j5)] 2.   sinh[ln(8 + j0)] + cosh(8ej0.785)

A: We need to solve the following complex numbers. Note: We will be using the trigonometric and…

Q: Question 9: Given that z = cos + i sin and u- iv = (1 + z)(1 − j²z²). Show that V = utan 30 2 r = 4²…

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Q: Find the quotient z1/z2 of the complex numbers z1 = 5(cos 4π/3 + i sin 4π/3)z2 = 10 (cos π/3 + i sin…

A: Given,   z1=5(cos4π3+i sin4π3)  andz2=10(cosπ3+i sinπ3) To find quotient z1z2: We know that,…