B) Find real numbers x, y, z for the identity below 2xi + 2yj- 2i + 3j + 2k = 3i -j+ zk

Q: Find real numbers x and y such that iy 2 - i i + 3 1 + i ||

A:

Q: Use De Moivre's theorem to find the following: 4 i. [1+ v3i]" -3 ii. [-1+ v3 i]

A: Given that: i. [1+3i]4 ii. [-1+3i]-3

Q: Let z = 2 – 3i and w = -3 + 2i. (a) Find z + w and z – w. -

A:

Q: В. Let a %3 -в -2 1, Find a value for k so that the dot product of a with = Lk 1 4]is zero.

A:

Q: Prove: ∀R x>0 and ∀Z n > 0, there is exactly one positive real y such that yn=x.

A:

Q: 21) Find the area of a triangle fosmed from the twovectors a = L'+2j-k-.

A: Given, a ⇀=i+2j-kb⇀ =2i-j+4k

Q: Find all numbers z such that Az3 + Bz² + Cz = D %3D B = [2 4 21 1 1 1. A = 1 3 1. 1 -2 2 4 21 C li 3…

A:

Q: Q: Show that the functi on f:R →R given by f (x) = ax +b, where ab e R, a #0 is a bijection.

A:

Q: An analytic function of a complex variable z = x + iy is expressed as f(z) = u(x, y) + iv(x, y).…

A:

Q: 2) Let R' real numbers, define = x,Y1 + 3x2y; + 5x3y3 for x = (x, X2, X3) and y (y,Yz, Y3). Is…

A: Given x=x1,x2,x3, y=y1,y2,y3 in ℝ3. Define x,y=x1y1+3x2y2+5x3y3

Q: 2) Let R real numbers, define = x,Y1 +4x2y2 + 6x3Y3 for x = (x1,x2, X3) and y (y1,y2, Ya). Is inner…

A: Let V be a vector space over ℝ.An inner product <·,·> is a function V×V→ℝ with the following…

Q: Find all positive integers x, y, z satisfying x · y · z² = 5xyz. '*

A: Introduction :Given , positive integers x,y,zwe have asked to find the values of x,y,z which…

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: Discuss the cosets of { (x, y) | x, y E R, x = y } in (R × R, +).

A: {(x,y) / x,y∈ℝ , x=y} in (ℝ×ℝ,+)

Q: Find the Avorare valne of Hhe famdtiun en the interal [ 0,4J VI+ 2x

A: Average value of the function on a given interval is 1/(b-a) integration of a given funtion…

Q: Prove that Ix I - I y I ≤ I x - y I.

A: We have to prove that  x-y≤x-y We know, x+y≤x+y Then,  x=x-y+y⇒x=x-y+y≤x-y+y⇒x-y≤x-y

Q: Prove that H(x, y) = (x, –y) provides a conjugacy between x' = (4 })x and Y'= (; 7). X and Y' = 1 -1…

A: Given: X' =11-11XY' =1-111Y To prove: H(x,y) = (x , -y) provides conjugacy between both of the above…

Q: Let z2T3-L p=S+Si O fird all the complex mumbers %3D guien by hza

A:

Q: السؤال 3 cos (z) =cosh (z) 0 صواب ihi O السؤال 4 The conjugate z of z=x+iy is z=x- iy صواب ihi O

A: 3. cos(z) = cosh (z) is FALSE

Q: Prove that da(x) = a(b) a(a), %3D |

A: This is a problem from Reimann Stieltzes Integral

Q: |(u+ v) x (u – v)I = 2|u x v|

A:

Q: prove that two vectur ae orthognal A = x + 4y+32 B =4x+2y-42

A: See the attachment

Q: a) Compute the absolute value and the conjugate of z= (1+i)°

A:

Q: 7. Derive the harmonic conjugate of u(x, y) = x² - y2. (2 2

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Q: Let ū = 2i – k and ī = i+3j + k. Compute |ū], |T], ū x ī, and Projzū.

A: Solution is here

Q: Example 3: Find real numbers x, y and z such that xi + 2yj – zk + 3i – j = 4i + 3k

A:

Q: 2-Express each function in the form u(x, y) + iv(x, y), where u and v are real, (c) ez2 (d) In(1+…

A: We have to write in u(x,y) and v(x,y) form.

Q: Dimension of ker A is Rank of A is

A:

Q: Give an example of two denes not equal X subsets of (R,T) and (z,7or ). ( Explain your answer ). cof…

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Q: If Z=1//2+j/v2 then the value * ?=of conjugate of Z^5

A: According to Euler, the complex number of the form cosθ+isinθ can be written as eiθ. The conjugate…

Q: What is the midpoint between z1 = 9i and z2 = 4? (2, 4.5) (-4,-9) (-2,-4.5) (4, 9)

A:

Q: T is self - adjoint then (Tx, y) is complex O normal O real O prime o

A: T is self adjoint

Q: Find the harmonic conjugate of u where u(x,y)=x^2 - y^2 -2xy-2x+3y

A:

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

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

Q: Use DeMoivre's Theorem to find the following. Write your answer in standard form. V2 cis- 20 O…

A: Given (√2cos(9π/20))5

Q: b- Let X₁, X2,... X (a) Find a comp (b) Find the UM

A: Solution:   (a):

Q: Let a, y, z be positive real numbers such that r +y+z xyz. Prove that 1 1 1 1 1 1 1+ x2 1+ y2 1+ 22…

A: Given- x + y + z = xyz This inequality can be proved by magic no. Concept-  First we will prove…

Q: If z = 3 – 3i, express 5/z  in the form a + bi

A: The given value of z is z=3-3i.

Q: zez Use Cauchy residue theorem to evaluate . (z'el + ) dz, C: 4x? + y2 = 16. %3D

A: We know that  z2e1πz is analytic throughout the complex plane. Hence by Cauchy's theorem ∮z2e1πzdz=0…

Q: Find the domain of r(t) = vt2 – 9i 1 j+In(1 – t)k. t + 4' O (-0, -4) U (-4,-3) O [-3, 1) O [3, 00) O…

A: The domain of t2-9 is t2-9≥0 or t2≥9 or t≥3 or t≤-3The domain of 1t+4 is t≠-4 (because denominator…

Q: let A=(ai)nxx be symmetric and positive definite. Show that dii >o, i = 1, 2, ...

A: Symmetric and positive definite matrix

Q: Find the area of S, which is the portion of the plane 2x + 3y + 4z = 28 lying above the rectangle 1…

A: We have to find the area S of the portion of the plane 2x+3y+4z=28 lying above the rectangle…

Q: Let f(x) = x5+ 3x4 + 2x2 and f(z) = 1024 + 1232i, the value of z is %3D %3D 2+ 4i 2-4i O 3+ 21 1+ 2i

A: We know, a+b5=a5+5a4b+10a3b2+10a2b3+5ab4+b5 a+b4=a4+4a3b+6a2b2+4ab3+b4 a+b2=a2+2ab+b2 i2=-1, i4=1

Q: 4. Use the algebraic description to find the image of AMNO). (x, y) → (x + 2, y - 3) M y

A: From the given figure, the vertices of the triangle are O-1,0,N-3,1 and M-2,4. The given algebraic…

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

A: Given z2 = 3+i and z3 = 1+2i

Q: a) Check that the functions e^x, e^-x,coshx are solutions of y'''-y'=0 b) show directly that…

A:

Q: If z=2e(i pi/20), use De Moivre's theorem to compute z5

A: Use demoivre theorem

Q: A space ship travels at 25 miles per hour and traveled continuously for 211 hours. 4 Enter the…

A:

Q: Use Gramer's Rule to Find K,y and Z -y-22 = -8 %3D + 32 = 2 %3D 7X +y+Z = 0

A: As per our guidelines we are supposed to answer only one question at a time. So submit the other…

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.