Reduce Z= ( 1+i) (1+i) / (1-í), to the form a + ib -1-i .a 1-i .b 1+i .C -1+i .d others .e

Q: -1 -2 -3 2 3 5 6 1 Let A = 1 Compute A-1 using adjoint.

A:

Q: 1 リ=ス,メ=0; Xe2, y=or abt. A the x- Axls

A: Given

Q: 4. Let z = -4 + 3i and zw = -7 – 2i. By showing clear steps, find w in the form of a+bi.

A:

Q: Find all values of z for which z* + 2 – i2v3 = 0 and represent them geometrically.

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Q: 37.) Show all step to evaluate: SN NS /3-y² /3-y² dzdxdy

A: We have to find the value

Q: Prove that Eo 2i = 2n+1 – 1 - i3D0

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Q: Prove that (x - i) = > xi i=1

A: We will prove the following result.

Q: Prove that x4+4=(x+1+i)(x+1-i)(x-1-i)

A:

Q: How many elements are in Z5[i]/<1 + i>?

A: Given Data The expression is Z5[i]/<1+i>.   Consider the Z5[i]/<1+i> in the form of…

Q: Let Let z, = 2-2i ,z, , Z2 =-1-3i find Find 1) 3-i) 2) Arg Z2

A: The complex number is of the form a+bi where a and b are real numbers and i is called iota whose…

Q: If {an} and {bn} are divergent, then {anbn} is divergent.

A: Given; (an) and (bn) are divergent.

Q: Prove that if |z| = 3, then %3D 5 2z – 1 7 - 13 4+ 22

A: The given is related to complex numbers. The solution is explained below.

Q: a+ib a) If x+ iy = prove that x? + y² = 1. a-ib

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Q: (b) 1 = -4 - 4- 2.

A: Given that

Q: Evaluate the integral. 2 (3u - 5)(u + 2) du -1

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Q: 1-a*** a zi i. La 1-a

A:

Q: Q4: 1- Prove that (1-0+(1+ () 0. 2. Put in the form a+ib ((1+i))- ((1-i)).

A: Here we have to prove that, 1) 1-i2+(1+i)2=0 2) Put in the form of a+ib, 1+i22-1-i22

Q: z = ecos(2x)

A:

Q: In evaluating | x(4 – x)3dx , if we use the substitution that u = 4 – x, then what will be the…

A:

Q: Prove Theorem| 2.3: (i) (A+ B)" = A" + B", (i) (A")" = A, (iii) (kA)" = kA".

A: To prove the given transformations

Q: ez = -2

A:

Q: 2, z) = 5 and the surfac e at (1,2,3). Evaluate = reasons).

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Q: Show that (AB)¹ = BTA¹ if A = 2 0 2 0 and B = -1 1 15) -3 1 -1 -1 2 2). a

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Q: 7. Find a pair of integers (x,y) such that 4021x + 2014y= 1.

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Q: Show that for all z1, Z2 E C, Then we have: |Iz1| – |z2|| < |z1 +z2l

A: 2) The inequality can be proved as follows:

Q: 2. Transform this LP into its DUAL counterpart. min 3x, + 2x2 - X3 subject to X1 + x2 = 5 -1 < x, <…

A: Transform this LP into its DUAL counterpart. Our problem can also be viewed as,   MIN  3x1 + 2x2 -…

Q: (2) Suppose that G, C Zn-r. Then prove that G,-1C Zn-r+1

A: We prove that

Q: +o0 - Find Ul-1/i, 1/i]- i=1

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Q: Prove that x' +4=(x+1+i)(x+1-i)(x-1+i)(x-1-i).

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Q: Is z(√2) isomorphic to z(√3)?

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Q: 34. Prove parts (a) and (c) of Theorem 3.2.3.

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Q: Find A'A and AA". -1 1 4 A = 2 0 2 (a) ATA (Б) ААТ Which of the products are symmetric? (Select all…

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Q: Find (a) ATA and (b) AAT. Show that each of these products is symmetric.

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Q: 3) Compute A-1 using adjoint. -1 -2 -3 -41 1 2 3 Let A = 5 1 0 0

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Q: homogenous DE 3udv-vdv-udu-vdu=0

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Q: In(z,) + In(-v3 – 1) = In(2) +i %3D

A: Answer

Q: 1: Find Z by convolution theorem. (z- 2)

A: convolution theorem

Q: Find a number z that satisfies: |z| - z = 2 + i

A: Complex number which satisfy |z|-z= 2+i

Q: Consider z1 = 1 - j2 and z2 = -2 + j3. Determine Im (21)?

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Q: 2 (x) 2. prove that s

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Q: 4-5. Evaluate the Integral 31) dt

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Q: x, and x, in terms of t.) 2 1 -1 1 1 -1 1 2 1 2 2

A:

Q: Prove that JI = J [1 0 0] I = |0 1 0 Lo 0 -1 2 -31 J = 4 5 -6 %3D –7 8 -9 1.

A: Considering the matrix multiplication of J and I

Q: (2.) Find another representation in which a. r is negative and 0 <0 < 2n. b. ris positive and -2n <0…

A:

Q: Let z, = 4 – 2i ; z2 = 3 + i ; z3 = 1 + 2i || -

A: Given z2 = 3+i and z3 = 1+2i

Q: Express 3x, xπ, and xsin x using the base e.

A: Our Aim is to express the following function using the base e given below:-(i) 3x(ii) xπ(iii) xsin x

Q: z, Z2 Prove

A: If z =x+ iy then  z = x- iy. i2 =-1.

Q: O Compute z = (1-i)"(13+i)

A: