If a rotation quaternion is [0.866, 0.162, 0.382, 0.279], what is "n-hat"? O [0.866, 0.162, 0.382] [0.162, 0.382, 0.279] [0.324, 0.764, 0.558] [0.081, 0.191, 0.140]

Q: Use the fact that 4 cos2(2π/5) + 2 cos(2π/5) -1 = 0 to prove thata regular pentagon is…

A: Given : 4cos22π/5+2cos2π/5-1=0 To prove: Regular pentagon is constructible .

Q: Consider the ordered bases B = {(1,2), (–2, 1)} ß = {(1, 2), (– 2, 1)} and B' = {(-7,6), (1, –8)} B'…

A: Given that  β=(1,2),(-2,1) and β'=(-7,6),(1,-8) are two bases for ℝ2.  Also give that…

Q: Which of the following is not an indeterminate form ? 33 8|800108 OO OO

A: Let's find.

Q: (a) {z: |z+2i| 6}

A: I have solved by drawing the diagrams. See the step 2

Q: 2. ) If a = 3i, b = i+j, c= i – 2j then: a) Find a + b + c in in i, j form. b) Find b + 2c in i, j…

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Q: In the group G = Z24, let H = (4) and K = (8). (a) State the Third Isomorphism Theorem. (b) List the…

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Q: Ex. (1): the paralel Sum and difference of the given complex numbers. 1. 2. 3. U = 2+3: U = 4+7i…

A: To add complex numbers in rectangular form, add the real components and add the imaginary…

Q: Q1) Consider two rotations, one about X by 30 degrees and one about Y 60 degrees: Are Rx Ry = Ry Rx…

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Q: Reduce to Canonical form Ur + 5 Ury + 6 uyy = 0 None UgE = 0 Uen = 0 = 0

A: compare the given equation with Auxx+Buxy+Cuyy+Dux+Euy+Fu=G therefore, A=1,B=5,C=6 find B2-4AC…

Q: One of the following is an ideal of z1: (0,3} (0,2,4,6} None (9,3,6,9}

A: From given statement

Q: iii) modulus of complex z = e"H equal to а. 3 b.2 С. 1 d. 0

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Q: Find the g.c.d. in Z [i] of 2 and 3+ 5i.

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Q: Find the legend re polyromial of 1-24 Ca , E1,i7 Fx) = - 3 - 3 SinlTx) -I los () -E Cu Pn(x) %3D

A: Given fx=-3-3sinπx-cosπx2

Q: 4.] Find PIAJ if A = Co,bicd)

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Q: {1,3, 5, 7, 9, 11}. Use the Let X = {4, 5, 6, 7, 8, 9} and Y roster method to describe each of the…

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Q: Write the following equations using index notation and Einstein summation convention: (a) (a b)(b c)…

A: The following are the rules in the Einstein's summation convention having the index notation:1) The…

Q: Let z be a non-zero complex number. Then Log(z²) = 2Logz for all complex numbers O if OSArg(z)ST/2 O…

A: We know that  log(z1.z2) =logz1 +logz2 iff -pi<arg(z1) +arg(z2) <pi

Q: find the conjugate of 2(cos7pi/12 + isin7pi/12)

A: Given expression: 2(cos7pi/12 + isin7pi/12)…

Q: Determine all the symmetries of r = 4 sin(1 + cos: 30).

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Q: Reduce to Canonical form y² Ur – 2 y Ury+ Uyy = Uz + 6 y O Um = 0

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Q: Given that z = cos + isin and u-iv-(1+z)(1-22). Show that 30 v = utan 2 r = 4² cos² (2). where r is…

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Q: 0,1,0) R3 Ba

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Q: REMOVE vectors from Ac (P,[R], +,). To obtain a BASE for (P.[R],+,): of the items 25 and 26 (Item…

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Q: 4. This question has two parts. a) Compute the value of eln 2020+3xi/4 b) Find all complex numbers z…

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Q: ?:R3 →R2,with? ?,?,? =(?+2?+3?,4?+?−2?) Find a basis for the image and state its dimension.

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Q: Re-express the following complex numbers in the x + iy form: a) z = 3e²(1 + b) z = e(in/4) + In 3 +…

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Q: Find a basis for Nul A, if 1121 A= 1 1 2 235

A: Let  Let Recall  the definition of Null  space  of  A.Null, null space of A. Using  the  above…

Q: Show how you find the Kernel and Image of T. Then verify dim Ker T and dim Im I you obtained by…

A: In this question, we have to find the Kernel and Image of any given linear transformation T and…

Q: 1. Write (2 + i) (4 - 3- 21 in the form a bi, where a,bR.

A: Value of i 2 = - 1 And i 3 = i   ( a - b ) 3 = a3 - b3 - 3 ab ( a - b )

Q: Tutorial Exercise Determine whether the series is convergent on Š1+ 10" n=1 Step 1 The series 1 +…

A: To solve the following problem

Q: iven that use the bhi tzS to compute %3D irst shifting Theorem [e"e cos 7+]

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Q: Find another representation of (5, pi/4) in which r is positive and 2pi<theta<4pi

A: Here we will find another representation for given point location,

Q: In the group G = Z₂24, let H =(4) and K = (8). (a) State the Third Isomorphism Theorem. (b) List the…

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Q: Let i = (6, – 6, 1) and v = (– 5, 5, – 6). %3D Compute the following: i · i = i. i = - 6(ü - i) = (–…

A: To evaluate the given dot product of vectors u and v.