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

Q: ind the three positive numbers I, y, and z with minimal sum whose product is 64.

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

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

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Q: Explain why the fundamental theorem of algebra does not apply to f(x) = Vx + 3. That is, no complex…

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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: 1. If f is the map that sends each complex number z = x + yi → y x Show that f(z1z2) = f(z1)f(z2),…

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Q: Draw the bifurcation diagram for i = (x – 3)(c+ x)

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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.

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Q: 1.) a) Find the roots of the equation z' +(1+ \3i) = 2z+1 b) Sketch the set Im <1 and determine…

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Q: 4. Find the harmonic conjugate of u where u(x, y) = x2 – y? – 2xy – 2x + 3y.

A: We will answer the first question since exact one was not specified, Please resubmit the question…

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

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Q: 1). Let, 2=x+iy *,y€R. In this case, (a). Prove the equations 2-2+2 and a = i.2 %3D %3D

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Q: b- Let X₁, X2,.... Xn b (a) Find a complete (b) Find the UMVU

A: Solution:   (a):

Q: 13R Q2 Put the complex number Z = 2e in the "Cartesian" form Z a+ bi where a, b E R.

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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: Find all the numbers z such that e^2iz= 5i.

A: We are given : e2iz=5i Now Using  Euler's equation: ( eix=cos x+i sinx) ⇒e2iz=cos (2z) +i sin(2z)…

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: Let the SPline function ConSider Sa)=a;+(x-x;)bi+(k-xi)Ci+ (x-Ki)dite; sin Ck-xi} Then find Sexi)=y;…

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Q: D dz |z|=1 |z-a|² 2

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Q: Let Y; and Yk be two principal components with associated 1; and Ak . Assume that Ak > lj. Which of…

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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: 2 A = 1+i 3

A: Given matrix is A=21+i1-i3 let the eigenvalue is λ. So…

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: 1. If z = x + iy is a complex number. (a) Verify that v2|z| > |Re(z)| + |Im(2)| [Hint: Reduce this…

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

A: See the attachment

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

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

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Q: Let x and y be positive real numbers. Prove that a + y > 2/xy.

A: See solution below

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

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

A: T is self adjoint

Q: For z=1+i find the product of z and its complex conjugate zZ

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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: Draw the bifurcation diagram for i = (x – 3)(c + x)

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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: Let A be a fixed constant positive number andf be an entire function with the property that |f (z)|…

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Q: Z-1 %3D ,then prove that x2 + y? = (x-1)2+y2 (x+1)2 +y2 (1) If Z %3D Z+1

A: Topic- complex number Note:- as per our guideline if more than one question uploaded than only first…

Q: Determine the image of the set S under the given complex mapping w = f(z). i) f(z) = 7 ; S is the…

A: We have the complex mapping : w=f(z)f(z)=z¯ S is the line y=x Let x=t , then y=t Let, z=x+iy…

Q: Determine the image of the set S under the given complex mapping w = f(z). i) f (z) = z ; S is the…

A: As Many Questions are given , I will solve only one : We are given the complex mapping:w=f(z)f(z)=z¯…

Q: Show that f : R → R is bijective, where: f(x) %3D필

A: A function is injective if f(x)=f(y)⇒x=y. A function is onto if for every y in Y there exists a x in…

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: determine where the given complex mapping is conformal. 2. f(z) = cos z

A: According to our guidelines we can answer only three subparts, or first question and rest can be…

Q: I. Solve using De Moivre's Theorem. Given that z is not real number and z = 1, show that w = z-1 z+1

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

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Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.