5. Find and sketch on the complex plane the 7 seventh roots of 128. Repeat the operation for 128j. Hint: Express 7 as 7e2nk for k = 0, 1, 2,, 6 (Why is this correct?) and find the roots for each case. The roots must all fall on a circle on the complex plane. How would you do similarly for 128j?

Q: 2. Write down the complex (a) 3+ j4, (b) 2 j. [(a) 3 -

A: See the details solution in below

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Q: Let i denote the square root of-1. For the two complex numbers z = 3e and w = 6e find z. w. Give…

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Q: 1. Solve the following complex roots and plot the solutions if

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A: Product of two complex numbers (a+ib)(c+id)=ac-bd+i(ad+bc)

Q: Using the given complex numbers on the Argand diagram find: Z4 -2 2. 3. Z5 21

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Q: What we want to do next is to write a procedure to raise any complex number to any integer power (x…

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Q: 5) Compute the fllowing complex numbers in standard arbi form for a, bE R. List all values if there…

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Q: 1. Determine the two square roots of the given complex numbers in Cartesian form and show the…

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Q: In an Argand diagram, O is the origin and the points P and Q represent the complex numbers z1 and z2…

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Q: O Given the complex number z=x+yj, 27 If Arg (z+1) = and Arg (z – 1) = = 3 Determine z. Express your…

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Q: 2) Suppose 1 and w are complex numbers, show that Aw =

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Q: of the complex number: (27V3 27 3

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Q: bi is raised to m if Find the imaginary component if the complex number a + a = 6, b = 6, and m = 7.

A: We have to find the imaginary component if the complex number a+ib is raised to m if a=6, b=6, and…

Q: The Complex number z is defined as 2- il1+i](1-2;) gven tnt (2-3i)+ p(z-3)=7FE where Paud 7 are real…

A: The complex number z is defined as z=i1+i1-2i2

Q: Every complex number a has a 4-bth root in C That is, there exists a complex Mumber w such that…

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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: Consider the following. Cube roots of -32V2(-1 + ) (a) Use the formula z = V7(cos 0 + 2xk 0 + 2xk +…

A: We first write -322(-1+i)=322-322i in the polar…

Q: A complex number is given as 2 + j2. The argument that results from taking the 5th power of it is…

A: Introduction: The complicated numbers are represented through a Cartesian aircraft referred to as…

Q: Find the modulus and argument of the following complex number. z=(3-2j) (1+2j), giving the principal…

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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: 4 Get all the roots of 2(V3i – 1) |

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Q: Find all the roots of z = -4 + (4V3)i giving each root in the form re". %3D 8° = -4+ (43) C

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Q: 8. Consider the complex number z = 2 + i and w = 7 – 2i. Write down the real and imaginary parts of…

A: Given : The complex numbers z = 2 + i  and w  = 7 - 2i.   To write the real and imaginary parts of…

Q: GIVEN: z = -6i – 11, determine the following: 1. zi, graph the roots on the complex plane, joining…

A: 1.

Q: 9. (1+iv3). 1/3

A: To find (1+i3)13

Q: bers are conjugate. If z, and z2 are two non-zero complex numbers st jal arg (2) ) - arg (z2 ).

A: Since we know that, | Z1 + Z2 | = |Z1| + |Z2| only when the the point Z1 , Z2 and origin are…

Q: Find the real component if the nth root of a + bi is determined for a = 9, b = 5, and n= 4. Round…

A: The given problem is to find the real component of the complex expression with given unknown…

Q: Determine the roots of the complex numbers studied in class. 28. z5 = 4i 29. z5 = 6i

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Q: 5. (a) Let z = (a + ai)(b+ bv3i) where a and b are positive real numbers. Without using a…

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Q: - Find the roots of the following complex nos. 3. %3D 3. Z =\ Z-27-0 %3D 3. |

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Q: (b) Find the conjugate and modulus of the following complex number Z = /5+ i6

A: Given complex number is z=5-i6 Since, conjugate of a complex number a+ib is a-ib Hence, conjugate of…

Q: Find and graph all the roots in the complex plane. 3. (3+ (4)

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Q: Q5: Find the first six roots for the complex number (Z): z°-z'+4z* - 6z°+ 2z² – 8z + 8 =0 |

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Q: Draw all eight solutions of z8 = 1 in the complex plane. What is the rectangular form a+ ib of the…

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Q: B- The Modulus and Argument of a Complex Number Z is (8, 90°) respectively find Vz4

A: We will find out the required value.

Q: Find the imaginary component if the nth root of  a + bi is determined for a = 9, b = 3, and n = 6.…

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Q: Find the real component if the complex number a + bi is raised to m if a = 5.6, b = 3, and m = 5.

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Q: Find and graph all the roots in the complex plane. (3 + i4)5

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Q: 1. Find all complex 4th roots of -8 – 8/3i, plot their location in the complex plane and show that…

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Q: If a = 2 + 10i, b = 4 – i, determine a²b³. Use all the roots of complex number b.

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Q: FIND THE ARG(Z) 0F THE FOUOWING compLEX NUMBERS

A: Solution

Q: Find the imaginary component if the nth root of a + bi is determined for a = 10, b = 8, and n = 7.…

A: Imaginary component of the function

Q: : Find the roots of the complex number: (27V3 27 2

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Q: Let 1 M = 1 Find formulas for the entries of M", wheren is a positive integer. (Your formulas should…

A: The given matrix is M=1-771. To find the higher power of the matrix, we need to diagonalize the…

Q: Given 23TO630" and H4151 What is the resultant of the given complex numbers? In rectangular form…

A: 6) Given: z1=6∠30° and z2=4+5i First express z1 in rectangular form. z1=6∠30° implies magnitude of…

Q: For the complex number z =2ej(-125)° what is Im{z}?

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Q: Find two square roots for the following complex number. 64 cis a Wo W1 = II

A: Given complex number is, z=64cisπ⇒z=64cos(π)+isin(π)⇒z=64(-1)=-64

Q: what are the complex numbers z1 and z2? for z1 i got z1= 3(cospi/12 + isinpi/2), z2= 2(cos7pi/12 +…

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Q: Let i denote the square root of –1. For the two complex numbers z = 3e 3 and w = 6e'3 find z. w.…

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