Consider the following. Square roots of −49i (a) Use the formula zk = nth root r [cos ((θ + 2πk ) / n) + i sin ((θ + 2πk ) / n)] to find the indicated roots of the complex number. (Enter your answers in trigonometric form. Let 0 ≤ θ < 2π.) (b) Write each of the roots in standard form.  (c) Represent each of the roots graphically.

Q: Write the complex number 4 COS 7π 4 7π + i sin 4 in the form a + bi.

A: Complex numbers is given in form of a+bi.

Q: Given the two complex numbers: 2₁ = 2 + 4i and Z₂ = √5 -3i 1) Find the value of the complex number…

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Q: tan¬1(z3) O 1.6293 - 0.3856i O 1.7644 - 0.6938i O 1.3390 + 0.4024i O 1.2969 + 0.5153i

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Q: Use De Moivre's Formula to compute the three complex cubic roots of v3 + i. List your answers in the…

A: To find: complex cubic roots of given complex number.

Q: In(In z1) O -0.5198 - 0.7636i O 1.4979 - 0.4636i O 1.5680 - 0.8205i 0.4498 - 0.3002i O O O

A: Let z=x+iy be a complex number. The polar form of the complex number is z=reiθ, where r=x2+y2 and…

Q: Consider the following. 7i(1 - V51) (a) Write the trigonometric forms of the complex numbers. (Let 0…

A: Given: Let, z1=7iz2=1−5i

Q: (a) Use the formula zk = Vr(co e+ 27tk cos +i sin 0+277K to find the indicated roots of the complex…

A: Given Z=-322(-1+i) Zk=rncosθ+2πkn+sinθ+2πkn, 0≤θ&lt;2π The trigonometric form of the complex number…

Q: Find the four fourth roots of z = 16(cos 60 degree + i sin 60 degree ).

A: Given  z=16cos60°+isin60° To find the fourth root De Moivre's theorem for finding complex root is…

Q: Solve the following  inverse trigonometric and hyperbolic complex numbers in their rectangular form.…

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Q: Given the two complex numbers: z1 = 6(cos π/2 + i sin π/2) and z2= 3/2(cos π/4 + i sin π/4) Find the…

A: we have to find

Q: Solve the following  complex numbers in their rectangular form

A: Given,             Z3Z2 Where in Z2 = 5e2i and Z3 = 4 cos 40°

Q: Consider the following. 3 + 4/ 1-V3i (a) Write the trigonometric forms of the complex numbers. (Let…

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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: Use the trigonometric form of a complex number to show that z-n = 1/zn , where n is a positive…

A: To prove the given identity

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: Consider the following. Square roots of 7(cos 120° + i sin 120°) 0 + 360°k cos 0 + 360°k to find the…

A: Topic‐ complex number

Q: Find the argument of the complex number 3/3 – 3i in the interval 0 <0< 2. Express your answer in…

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

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Q: Solve the following complex numbers: Z1 = 5+3i ; Z2 = 4+5i ; Z3 = 3-i %3D

A: Givenz1=5+3i ; z2=4+5i ; z3=3-i

Q: Vz1 (principal root) O 4.3525 - 1.0275i O 4.3525 + 1.0275i O 2.0582 - 0.4859i O -2.0582 + 0.4859i

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Q: Find three cube roots for the following complex number.    27(cos 120° + i sin 120°)   w0= w1= w2=

A: We find out three cube roots of given complex number using z1/3=r1/3(cos…

Q: - Find all the complex roots of (-5+4i)*/ª

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

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

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Q: Solve the following complex numbers: Z1 = 5+3i ; Z2= 4+5i ; Z3 = 3-i 1.The roots of (Z3)^(1/3)

A: I am going to solve the given problem by using some simple algebra to get the required result.

Q: Solve the following  complex numbers in their rectangular form.  Where in Z1=2+4i, Z2 = 5e2i and Z3…

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

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Q: Find all the complex fourth roots in rectangular form of w = 64 cos +i sin %3D (Type your answer in…

A: To find the fourth root of the given complex number.

Q: Consider the following. 1 + V3i 5 - 3i (a) Write the trigonometric forms of the complex number. (Let…

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Q: From the topic of Trigonometric of Complex Numbers. Evaluate tan-1(1+j).

A: Given  To evaluate tan-11+j

Q: Consider the following. Square roots of 5(cos 90° + i sin 90°) (a) Use the formula zk = V r cos- 0…

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Q: Write the complex number in trigonometric form r( cos 0+ i sin 0), with 0 in the interval [0°,360°).…

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Q: For a positive integer n, the complex number z = r(cos 0 + i sin 0) has exactly n distinct nth roots…

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Q: Find all the complex square roots of w= 9( cos 45° + i sin 45°). Write the roots in polar form with…

A: Let's Solve,

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: Evaluate the complex number sin(0.346 – 0.548i), -

A: We know that  sin(ix) = i sinhx,   and  cos(ix) = coshx  sin(A-B) = sinA cosB - cosA sinB

Q: B. Find the indicated powers and roots, giving the results in algebraic f 1. [2(cos1500 +isin…

A:

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: Convert the Complex number 10V3- 10i to trigonometric form: r(cos(0) + i- sin(0)).

A:

Q: find all complex values z satisfying the given equation cosh z = 2+3i

A: We know that - cosh x= (ex-e-x)/2 using it, the explanation is given below-

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

A: Root of complex number

Q: logz, (z3":) \0gz;

A:

Q: Consider the following. (2 + 21)(1 – 1) (a) Write the trigonometric forms of the complex numbers.…

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Q: Consider the following. Square roots of 4(cos 90° + i sin 90°) 0 + 360°k (a) Use the formula z =…

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Q: Find all the complex square roots of w 9( cos 45° + i sin 45°). Write the roots in polar form with 0…

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Q: Consider the following. 1 + V3i 5- 3i (a) Write the trigonometric forms of the complex number. (Let…

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Q: Consider the following. Square roots of 16(cos 90° + i sin 90°) (a) Use the formula zk = V Vi( cos 0…

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Q: Solve the following  complex numbers in their rectangular form.  Where in Z1=2 + 4i, Z2 = -2.0806 +…

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Q: 2. What is the standard form of the complex number –13.5(cos() + i sin())?

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Q: 2. 8 cos + i sin 8 8 10 + i sin 16 cos 16

A: