Write the following equations using index notation and Einstein summation convention: (a) (a b)(b c) + (a.c) = t (b) a2b²+ (a - b)² = 1 (c) a × (b+c) +ex f=0 where 0 is the zero vector.

Q: Are the following two sets of coefficients orthogonal? -1, 0, 0, 1 -1, 1, 0, 0 Yes No

A: Given data is as follows: -1,0,0,1 -1,1,0,0 Yes the following sets of coefficients are orthogonal as…

Q: Perform the indicated operations and express the result in simplest form 3j2-j20+(10+j4)

A: Given expression is 3j2-j20+10+j4.

Q: (b) Show that i³i is real, even though i or 3i is not.

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Q: swer in polar form where r> 0 and

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Q: Show that A×(BxC) + Bx(CxA) + Cx(AxB) =0.

A: We have to prove that LHS=RHS

Q: Solve the complex equation (2+j)(3-j2)=a+jb

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Q: - j6) (60-j80) 2 329) EX(16

A:

Q: If z = 1+ 2i and w = 3+ 4i, express the following in the rectangular form: (a) 2|w| +(1 – i)2² w + z…

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Q: Find (a) u × v, (b) v × u, and (c) v × v.…

A: Given : u =0,2,1v = 1,-3,4(a) u x v = ijk0211-34u x v =i 21-34    -j0114  +k021-3          = i(8+3)…

Q: (c) Write (V3+ i)" in the form of x+ iy.

A: Here I have applied De Moivre's Theorem. See the solution.

Q: Find the conjugate of z = -2 – 4i, and compute zz. z = zz =

A: Given that: z=-2-4i

Q: 3/2n 7. Find proj in terms of: (a) b)

A: Solution of the problem as follows

Q: Determine |z| if z =2−3i.

A: z = x +i*y |z| = √(x2 + y2)

Q: Simplify the following expressions: (5-j6)-(2+j8) (-3+ j4)(5-j)+(4-j6) (a)

A: To Simplify: (a) (5-6j)-(2+8j)(-3+4j)(5-j)+(4-6j). As per policy, only the first part is answered,…

Q: Problem 5. Let X = [X1,..., Xn]' be a random vector where each component X; is a real-valued random…

A: Step 1: Let  X =[x1,x2,...xn]T be a random vector where each component xi is a real valued random…

Q: Evaluate the complex numbers j(3 – j4)* (-1+ j6)(2 + j)² (a) z1 1 +j 4 – j8 11/2 (b) Z2

A:

Q: Calculate the triple product ā · (b x c), where ā =,b=, and č=.

A: Given vectors  a→=2 , -4 , 1b→=0 , 3 , -1c→=5 , -3 , 3

Q: Find the real numbers x and y if (x – iy) (3 + 5i) is the conjugate of –6 – 24i.

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Q: Find curl (5z i + 6x j + 2y k). curl (5z i + 6x j+ 2y k) = ( i )i + ( i )j + ( i )k Save for Later

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Q: 17. Let f(x, y) = x'y4. Use Eq. (4) to estimate the change Af = f(2.03,0.9) – f(2, 1)

A: You have to just put the value in the function and proceed....go through the solution

Q: Find the distance d (in the complex plane) between z = 2 + 7i and w = 11 - 10 i. d = √ (1)² + (9)² X

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Q: Find curl (4z i + 5x j+ 2y k).

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Q: Verify that              a.(b x c) = b.(c x a) = c. (a x b) if               a =4i – 3j +6k ,  b=…

A: Given that a→=4i-3j+6k, b→=5i+4j-3k, c→=4i+6j+3k We have to verify that a→·b→×c→=b→·c→×a→=c→·a→×b→

Q: Express −i+j in the form [a,b]

A: Simplification

Q: Express the sum cos 3x + cos 2x as a product.

A: the given sum is: cos 3x+cos 2x we have to express the given sum as a product.

Q: Write a formula for a function f (x) such that f takes the square of the input, multiplies the…

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Q: Find the principal value of (2j)²j

A: The given  complex number is                                       z=(2j)2j We know that…

Q: Find (a) u + v, (b) 2v, (c) u − v, and (d) 3u − 2v. u = (−1, 2, 1), v = (0, 1, 1)

A: Given  u = (-1,2,1) , v = (0,1,1)Find   (a) u+v      (b) 2v      (c) u-v      (d) 3u-2v