Find the modulus and argument of the following complex number. z= (3+2j) (- 1+2j), giving the principal value in degrees to 3 d.p. A =V65, arg (z) = - 150.2550 B =/65, arg (z) = 150.2550 © I:l=/65, arg (2) = - 29.7450 D=/65, arg (z) =29.7350

Q: Determine the argument and the modulus of the given complex (-2-4i)(5i) number: (3+8i)

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Q: Determine the fifth roots of z = (4-j5)cos(1+j3). Express your answer in rectangular form

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Q: 4. Find the modulus, Iz], and argument, 0 , of the complex number. -1 + i

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Q: Find the modulus and argument of the following complex numbers. 3- 2j giving the principal value of…

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Q: Find the modulus and the principal value of the argument of the following powers of complex number:…

A: Explanation of the answer is as follows

Q: Find the modulus of the complex number. -5- i

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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: Solve the following complex numbers. 0 ≥ θ ≥ 2Π If z5 = 1 - 2i

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Q: Find the three cube roots of the following complex number: 120 ( cos60 + i sin60) O (4.63 + 1.69i),…

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Q: Find two square roots for the complex number. Leave your answers in trigonometric form. 81 cis 0° 9…

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Q: 13 8 cos 37 + i sin 8 |10 + i sin 16 Cos 16

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Q: How would I find the magnitude of the complex number based on the given values for z?

A: To find the magnitude of the complex number

Q: Solve the following  complex numbers in their rectangular form

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

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: of the complex number: (27V3 27 3

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Q: Find the modulus of the given complex number. 8. -2 - i

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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 the cube roots of the complex number z = 125 (cos(60°) + i sin(60°)). Select all correct…

A: We have to find cube root of given complex number.

Q: Find the modulus of the given complex number. Give exact answers only and show your work. -7 - 5i

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Q: Find the modulus (r) for the given complex number z = -6.3 + 8.2i.

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

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Q: ber with this given equation?

A: Here we have to find the magnitude of the complex number with this given equation. Given : z=-1+1i…

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

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Q: Express the following complex number in exponential form: (3 - 4) O -V5e-5.36/ 5e5.361 5e-5.36i…

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Q: he following  complex numbers in their rectangular form

A: Given,              logZ1Z3Z2 Where in Z1=2+4i, Z2 = 5e2i and Z3 = 4 cos 40°

Q: 1.) sec (-2.0807 + 4.5465i

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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 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: 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

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

Q: . Ifa complex number z has modulus 2 and argument , then

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Q: (3.0642+2.5712i)(-2.0806+4.5465i)

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Q: Simplify the complex number z = j(-1+ j) and plot the result on your Argand diagram. Then, find the…

A: Given :           z = j(-1 + j)        To simplify z and to plot the result on Argand diagram.…

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

A: Root of complex number

Q: Find the modulus, Izl, and argument, 8, of the complex number. -1+i One charaes 4.6

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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: To divide two complex numbers in trigonometric form, ________ their moduli and_____ their arguments.

A: If z1=r1cosθ1+isinθ1=r1cisθ1 andz2=r2cosθ2+isinθ2=r2cisθ2 are two complex numbers intrigonometric…

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

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Q: Evaluate the given complex number: 3i (4 – 5i) (6 cos 25° + 6i sin 25°) and determine the modulus…

A: The complex number z=x+iy in its polar form can be written as z=rcosθ+isinθ. Here, the modulus,…

Q: Find the three cube roots of the following complex number: 512 ( cos 60 + i sin 60 ) O (4.52 + 2.74i…

A: Solution

Q: VzI (k=1) O 4.3525 - 1.0275i O -4.3525 + 1.0275i O 2.0582 - 0.4859i -2.0582 + 0.4859i

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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: 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: Match the correct modulus or absolute value to the complex number: - 6 + 8i

A: Explanation and solutions is given below....

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: Divide the complex numbers below and leave t trigonometric form. 7(cos 150° + i sin 150°) 9(cos 190°…

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Q: Given the complex numbers z1 = 5 (cos(139°) + i sin(139°)) and z2 = 2 (cos(-94°) + i sin(-94°)),…

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Q: Exer. 21–46: Express the complex number in trigonometric form with 0 so<27. 25 2V3 + 2i 4 cis 37 29…

A: Given: The complex number 25) 23+2i. 29) -20i 34) -5.