1296. Express your answer in polar form Find the four fourth complex roots ofz = and then convert them into rectangular form. The exercise should be worked without the aid of a calculator. roots: 0, < 0, < 03 <0 21 = T;cis(0,) = a + bi

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

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Q: For the complex numbers z=8(cos 70° + isin 70°) and w=5(cos 210° + isin 210°), find the following.…

A: We know, for multiplying two complex numbers in polar form, we just need to multiply the moduli and…

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: Write the trigonometric form of the complex number. (Round your angles to two decimal places. Let 0…

A: Given: z = 77-i^  Comparing the given complex number with z=x+i^y, we get,  x = 77 , y = - 1. The…

Q: How may the following complex numbers be obtained fromz = x + iy geometrically? Sketch. 1 / z

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Q: Find the quotient z1/z2 of the complex numbers z1 = 12(cos 3π/4 + i sin3π/4) and z2 = 4(cos π/4 + i…

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Q: Find the three cube roots of -8i. Express your answers in polar form and the convert them into…

A: To find the cube root of -8i Let z = -8i

Q: In this question we use the complex numbers x = 1 + 2i, y = 3-i, 3π 3π √2(cos ³4+ isin ³7). Complete…

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Q: find the quotient z1/z2 of the complex numbers z1 = 10(cos 10° + i sin 10°) and z2 = 5(cos 5° + i…

A: The complex numbers z1 = 10(cos 10° + i sin 10°) and z2 = 5(cos 5° + i sin 5°). We need to find the…

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

A: Given:         z1 = 3(cos π/5 + i sin π/5)  and        z2 =  4(cos π/10 + i sin π/10)

Q: If X = 3 - j2     and    Y = 3 + j2   convert your pair of complex numbers to polar form

A: For X=3-j2:

Q: Take the last four digits ABCD of your student identification number, and let z1= A + Bi and z2 = C…

A: Here, z1=5i z2=6+4i

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…

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

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Q: Find two square roots for the complex number: 25(cos120degrees +isin120degrees) answer in…

A: Given, 25cos120°+isin120°

Q: Express the complex number z = 10 cis 315° in rectangular form a + bi.

A: Given the complex numberz=10cis315°

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: 8. Find the complex eube roots of 64 (cos 210P + isin 210°). Write yourn- swers cither in polar form…

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Q: 8(cos(30°) + sin(30°)i) , from polar to rectangular form. Convert the complex number, z = Enter your…

A: Convert from polar to rectangular

Q: Given a complex number w =. TM UTM UT iv3) by giving your answers in i. Express w in polar UT4 ii.…

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Q: |74. Notice that (r cis 0)² = (r cis 0)(r cis 0) = ² cis(0 + 0) = 2 cis 20. State in your own words…

A: Given that: (rcisθ)2=(rcisθ)(rcisθ)=r2cis(θ+θ)=r2cis2θ

Q: Find two square roots for the following complex number. Leave your answers in trigonometric form. 64…

A: Solution

Q: Convert the given complex number from the given rectangular to the polar form of r(cos 0+j sin 0).…

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Q: Find all complex numbers that are solutions of the given equation. Leave your answers in standard…

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Q: Convert the complex number in standard from to cis form r cis 0 Write 0 in degrees between ) <0 <…

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Q: 2. Find the Cartesian (x+iy) form of this complex number 3π 3π Z=4(cos + 2 isin 377)

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Q: Transform z =2- 4i into trigonometric, polar, and exponential form. %3D

A: Topic:- complex number

Q: Give an example of a reduced cubic in the form x = 3px + 2q with three real roots but where q – p³ <…

A: Question: Give an example of a reduced cubic in the form x3=3px+2q with three real roots but where…

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 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: hich of the following is equivalent to (3 +3i/3)"? (Hint: You may want to convert the complex number…

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Q: Find y as a function of t if 7y" + 28y = 0, y(0) = 4, y'(0) = 3. y(t) Note: This particular weBWork…

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: Calculate the coordinates of the centre and the radius of the circle represented by Iz+j*18]=5 where…

A: We know that z=x+jy and z = x2+y2 If equation is of the form (x-h)2+(y-k)2 = r2…

Q: Express the complex number z = 10 cis 270° in rectangular form a + bi.

A:

Q: Find all the complex square roots of w= 81(cos 30° + i sin 30°). Write the roots in polar form with…

A: Solution:- Complex root of w=81cos 30°+i sin 30°   wn=rcos θ+i sin θ wk=xr cosθ+2πkn +i sin θ+2πkn…

Q: Express the complex number z = –1 – V3i in polar form r cis 0. Select the correct answer below:

A:

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

A:

Q: Let z be a complex number. Then i(cosh(3z)+sinh(3z))=e^(3z)?

A: Explanation of the answer is as follows

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

A: Express the complex number

Q: Find y as a function of t if 3y" + 31y = 0, y(0) = 7, y'(0) = 3. y(t) Note: This particular weBWork…

A: A differential equation with initial conditions is called the initial value problem. The solution of…

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: Identify the Real and Imaginarg Part o the Complex number

A: Given the expression: z=(4+j3)sinh(3+j)+cos(3-j2) To find the real part and imaginary part of the…

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,…