The complex number Z is defined as follows: z = (1-√3i)² Calculate Z in polar form, where Z = |Z| (cos(0) + i sin (0)) Enter solution including 2 decimal places. Example if Z = 2 enter 2.00 |Z| = 128 0= O-5π/3 Ⓒ5π/3 ОTT/3 O-π/3 OTT O-TT

Q: 1. Find all 5th roots of the complex number -32i. Express your answers in complex polar form. For…

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Q: Find the produCtI' 22 n polar form, Wnerezi and 2 are BIVEN below. 21 = 4(cos(61"+i sin(61") 22 = 5…

A: According to Euler's identity, r ( cos x + i sin x) = r eix

Q: The complex numbers Z₁ and Z₂ are defined as follows: ²₁ = 5 (cos(²) + i sin(2)) ²₂ = = 2 (cos() + i…

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Q: 1. Consider the nonzero complex numbers z1 = 3i, z2 = 6i and z3 = 4i. (a) Evaluate (z,z,z3) (1 + z2…

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Q: 1) z = e(4+j3) lIn(6230°)

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Q: In polar form the complex number z = 3/2 + 3v2i can be expressed as (cos 45 +i sin 45 ). Let w = z3…

A: The given complex number,   z=32+32 i

Q: What are the solutions to x³ = -4+4i in polar form? Select all correct answers. □ 32 cis (19) □…

A: The Polar form of a complex number is r(cosθ+i sinθ) where r=x2+y2 and θ=tan-1yxx3=-4+4i=32.(cos…

Q: 4 - i (a) 7 r = , 0 = (b) –87(4 + i/3) r = ,0 =

A: Given:  a) 4-i7   The standard form of complex number is  =47-i7  For a complex number a+bi, the…

Q: In Problems 2 and complex numbers in surd form. 2. (a) 2+13 (b) 3. (a) -j3

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Q: (-1+√3i)* late Z in polar form, where Z = |Z| (cos(8) + i sin (0) ) solution including 2 decimal…

A: For a complex number  argument  and modulus Also note the following peroperty of complex number  for…

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: 9. Find the indicated roots. Sketch the roots in the complex plane: a) The fifth roots of 32 b) The…

A: According to Bartleby guidelines I can only answer the first question of the given problems

Q: The negative complex roots for the quartic equation x* +x² –1=0 are: 1-5 b. i + a. ti 2 c. ti 2 |1+…

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Q: The complex numbers ₁ and ₂ are defined as follows: 21 = 3(cos()+isin()) 22 = 5(cos()+isin()…

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Q: The roots of the complex number z = (2)¹/2 is Wo = √2 [cos+ i sin], w₁ = √2 [cos+ i sin true false

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Q: Give the solutions of the complex equation –3z°(1 + i) = z(1 – i) in trigonometric for

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Q: The complex numbers ₁ and ₂ are defined as follows: 2₁ = 3(cos() + isin()) 22 =2(cos(¹)+isin()…

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Q: Vector u has an initial point at (−5, 2) and a terminal point at (−7, 9). Which of the following…

A: The vector u has an initial point at -5, 2 and a terminal point at -7, 9. We have to find the…

Q: The complex numbers Z₁ and Z₂ are defined as follows: Z₁ = 3 (cos(−2¹) + i sin(−2π)) 4 4 ²2 = 2…

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Q: 2 Express (+) in polar form O 3 [cos 67+isin 67] O 13 [cos 70+isin 70] O 3 [cos 70+isin 70] O 13…

A: Given complex no. is 5+i1-i2

Q: 3. Express the following complex numbers in polar form( r< θ), find the modulus ‘r’ and argument θ”…

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Q: The complex numbers Z₁ and Z₂ are defined as follows: ²1 6 (cos(4) + i sin(4T)) = Z₂ Calculate = 12…

A: The given complex numbers are…

Q: The complex numbers Z is defined as follows: Z = (4-4)² Calculate Z in polar form, where Z = |Z|…

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Q: (a) Find in the form of re'", the six complex numbers which satisfy the equation z° +32+ 32( v3 )i =…

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Q: the complex number 6√3+6i in polar form 12(cos(n/6)+isin(n/6) 12(cos(n/4)+isin(n/4)…

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Q: Exercise 3: Let c16 = 3cis (0.7) and c17 = 2cis(1.2) (recall that the angels are in radians) : a.)…

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Q: 4) z = (4 + j3)sinh(3+j)+cos(3-j2)

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Q: The complex numbers Z₁ and Z₂ are defined as follows: (cos(²T) + i sin(2)) Z₁ = ²₂ = 9 0 = 0-2π/3 a-…

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Q: I. ) IF Z = (4<30) (6 < 140) . FIND z. (RECTANGULAR FORM» %3D (-3+5i) 2.) SOLVE 4<30)² (2cis60)3 (6…

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Q: The complex numbers Z₁ and Z₂ are defined as follows: = 0.5 (cos(-2) + i sin(-2)) 6 6 ²1 ²₂…

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Q: write z= -6+ 6t in polar form

A: z= r cos (theta) + r sin(theta) this is polar representation

Q: The complex number Z is defined as follows: Z = (1+√3i)5 Calculate z in polar form, where Z = |Z|…

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Q: The complex numbers Z₁ and Z₂ are defined as follows: = 4 (cos(²T) + i sin(²) ²₁ Z₂ Calculate = 8…

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Q: Can you correct what I did wrong in part a?

A: 1. (a) The problem done is fine, but the variable n can be changed according to choice. Explanation:

Q: 1. Find all solutions of the equation z2 + z +1 = 0.

A: Explanation of the answer is as follows

Q: Please solve this problem

A: For (a), We are given that α is a real number in the interval [0, 2π) and z = cos(α) + i sin(α). We…