5Express the following in the form a+ bi 3. G012-0141). Ans 016 i

Q: Solve the following equations in Z with x expressed in both standard and non-standard names: (i) xx…

A: (i) x•[5] = [2]  So, x = [2]•[5]-1  We need to find the inverse of [5] in Z6  In Z6 we have, [5]•[5]…

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

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Q: Define an by an for 4an-1 +5an-2, n 2, ao = 5, a1 = 13. Find an explicit formula %3D an

A: an=4an-1+5an-2 an-4an-1-5an-2=0 for the homogeneous system, write the auxiliary equation  r2-4r-5=0…

Q: Q2/ fincd lachre trans form for at X- 3x+2X=lee

A: given equationx"-3x'+2x=1-e2tby assuming that initial condition is zero.x"=s2X(s)and x'=sX(s)and…

Q: =[12] and U- = -[] Then A2017U is equal to -1 Let A =

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Q: 3 Given that u = 4i+ GJ and Iv[ = 2, find vif u and V are or thugonal to each other.

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Q: . Find Im(2z+4z-4i), in which ž is the conjugate of z.

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Q: Q3- Give an example of two denes not equal X subsets of (R,T) and (z, of ). ( Explain your answer ).…

A: Answere : The two example are given below :

Q: Q1: A. - Simplify the following complex relation to z -x+iy by finding the modulus (1+iv8) V24 +i…

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Q: Find the value of the Conj uction g(+) ifya know that w(f.g)=3e" and fCo=et (Wronskain)

A: We will find out the required value of g(t).

Q: 4. Consider the complex number w = 3cis (5). For which value(s) of k is x – wa factor of the…

A: I am going to solve the given problem by using some simple geometry to get the required result.

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

A: Solution of the problem as follows

Q: Prove that Zo is not isomorphic to Z 10 12

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Q: 5 ress the following in the form a+bi Express • (012-0141) Ans: 0.016 i 0.088 +0.

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Q: Q: Find the gcd (a, b) and find two integers x and y suchthat gcd(a, b) = ax + by. Ex.(i): a = 901…

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Q: Solve the folowing equation on [0,2pi) 2sqrt2 +4cosx=0

A: In the given equation, the cosine function is the trigonometric function:   Rewrite the given…

Q: b) By using De Moivre theorem, calculate in the form of a + bi: 4. i) (VZ – iv2)* | ii) (1– i)6

A: Given (2-i2)4 &   (1-i)6

Q: (2) Find all the numbers z such that elz = 10i.

A: Consider the given. eiz=10i

Q: the z-score for Omar's exam grade

A: The grades on a math midterm at Springer are roughly symmetric with μ=78 and σ=5.0 and Omar scored…

Q: ez = -2

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Q: Find a number t such that In(4t + 3) = 5 %3D

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Q: CALCULATE THE FOLLOWING USING MINOR COFACTOR AND COFACTOR EXPANSION 3 -8 2 A= 2 -6 3 4 4 2

A: A system of m×n numbers arranged in the form of a rectangular array having m rows and n columns is…

Q: Q1) If B = B-1 then B = I or B = -I. Prove or give counter example. %3D

A: A detailed solution is given below.

Q: tegers differ by 65, Their product is -966. an equation to represent this product. -her factoring or…

A: Let the first number be x , therefore second number be x-65 Now from question , Product of number is…

Q: PROVE that 2a + b = 0.

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Q: 9. Use the adjoint of A to find A', where -1 3 A =0 -2 1 -2] 1 Confirm your answer by showing that…

A: A=-1320-2110-2

Q: Solve the following quadrati c equati ons by factorizati on method: x+3 1-x 17 (ii) x-2 4

A: Quadratic equations by factorisation meyhod -

Q: the integret fector of the bifferentiel e qration →き x28x he is 2. O Not found

A: Consider the given differential equation xdy-ydx=x2y3dx and rewrite it again by doing…

Q: 5) Let A= 18 Using Caley-Hamilton theorem find the expression A* -19A³ + 18A? + A + 21.

A: Please refer the attached image for complete solution.

Q: Solve the followig 13. BauSsian or Eduss Jordan Using E lemination. 5x, +6x=7X 3D0 3. ース×,+ 3X7…

A: Answer

Q: Q2) n(x) = x1 , kx) = (x – 1)/2 , %3D %3D | 1-(8 + x) Find a formula for ( monok).

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Q: (5) Express ress the following in the form a+bi 3 (012 -0.41) ³ Ans: 0.016 i -0.088 +0. P

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Q: Use the adjoint to compute A- for 2. 3 A = | 0 2 -1 1 -2

A: A=2310112-1-2 Now determinant value is, A=2-2+1-30-2+10-2=-2+6-2=2 Now cofactors are,…

Q: Q.2 Solve the following set of equations x + 4 y + 3z = 2, 2x - 6 y + 6z = -3, 5x - 2 y + 3z = -5…

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Q: uppose A is a diagonali= . Would this be true if

A: Given, A is a diagonalizable n x n matrix whose eigenvalues are all 1 or -1.

Q: test the conver gehre and dvelyence n coscnt)

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Q: Which of the following is a cube root of – 2.3 – j1.25 1.3782 + j3.3075 -1.3593 - jo.2276 -1.3782 -…

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Q: Prove that Co +2C, +4C₂ +8C3 +..... +2 °C₁ = 3^

A: Given problem:- Prove that C0 +2C1+4C2+8C3+...... + 2n nCn =3n

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

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

Q: polynomial in V2+i and compute the conjugates of i over Express i as a Q(/2 + i).

A: As per the question we have to express i as a polynomial in (√2 + i) and then compute its conjugate…

Q: Q1: A. Simplify the following complex relation to z - x+iy by finding the modulus and argument form…

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Q: 2 Which of the following values of a will make |2 0 a non-invertible? -al

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Q: ALL ORK IOWN 19. State the conjugate of the following expressed in simplest a + bi form a) 2+ V-9 b)…

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Q: Find integers s and t so that s· 201 + t · 302 = 1 . S %3D

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Q: 2. 2. (xij-X-) Xij-.. prove thate

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Q: Q1. Prove that KT = = -.

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Q: 22. Use the adjoint of 1 -5 -1 A = 0. -2 1 to find A-

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Q: Compute the following powers and give your answer in the form a+bi (3 V3 3 = 0 2 2 | 123 = 0 1 V2 V2

A: Computer the powers.

Q: se Indirect Proof to prove that if a and b are both positive, and a2 < bi

A: