FOR ANY TWOCOMPLEX NUMBERSZ, ANDZ,,PROVE THAT |Z|+|Z,|=,(Z, +Z,)+ /Z,Z» +÷(Z, +Z»)- Z,Z, .

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Q: 5. Prove OR disprove that Z/2ZOZ/3Z is isomorphic to Z/6Z

A: To prove or disprove that  Recall that , Now to prove or disprove that  These elements of these…

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Q: 2. Find all number z such that Az" + Bz² + Cz = D a. A= 2

A: We'll answer the first question since the exact one wasn't specified. Please submit a new question…

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Q: Type here to search Check 2. %3D D = (-) + *** - ,(-) + ,(+-) + (+-)

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A: The greatest common divisor (gcd) is the largest positive integer that divides each of the integers…

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A: Given: 2+i To find:  The irr(ꭤ,ℚ) and deg(ꭤ,ℚ)for the given algebraic number ꭤ ∈ ℂ.

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A: If we take transpose of transpose matrix, the matrix obtained is equal to the original matrix.…

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A: Bijective function: The domain is set A and the co-domain in set B relates elements of two sets A…

Q: For complex number z and w, prove that zw-wz=z - w if and only if z =w or, zw = 1.

A: We know that , for a complex number|z|2=zz¯and when z is a real numberz=z¯

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A: Given:

Q: If |z|=1,show that (z^-1) =(z congegate)

A: Given z=1 We have to show that z−1=z¯ Since, z=1 ⇒z2=1 We know that z2=zz¯

Q: Suppose X has n elements and Y has m elements. How many bijections X → Y are there?

A: To find: The number of bijections X → Y are there. Given information: X has n elements and Y has m…

Q: Prove that if x+y=%30 then y=-x

A: See the attachment

Q: Find (a) projvu and (b) projuv. Use the Euclidean inner product.u = (5, −3, 1), v = (1, −1, 0)

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A: To prove, x·0=0

Q: prove that 2,

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A: For the solution of the problem follow the next step.

Q: #5 Let x, y, z be nonnegative real numbers such that y + z> 2. Prove that (x + y + z) >4x + 4yz.

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Q: 2 FIND PROJECてION マ=<2,8,97 THE OF く,2,37 ONTO %3D ( Use proper notation wer) in ans u your

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Q: Assume that (8) ∞∑n=1nanxn−1=∞∑n=0anxn∑n=1∞nanxn−1=∑n=0∞anxn for all x, and determine what this…

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Q: Question is attached, Thankyou

A: Let us take z = x + iy.

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

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A: Q8) Given: v(x)=x3+3x

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A: Intermediate value theorem:- If f is a function which is continuous at every point of interval a,b…

Q: Prove the

A: Follow the steps that I listed given below pitcher.

Q: Show that If |z| = 1, then: -1 = Z

A: z is a complex number. z=a+ib |z|=(a+ib)(a-ib)     =a2-b2 if |z|=1, then a2+b2=1

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A: Given:

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Q: Let x, y and z be real numbers. If x > y and y = z, then x > z. For any real numbers x and y, with x…

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Q: (ii) A = 82 + &V1+ 4

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A: A subring S of a ring R is a subset of R which is a ring under the same operations as R.   An ideal…

Q: or complex number z and w, prove that zf w-|wfz=z-wif and onlyif z = w or, zw = 1. W

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Q: A complwx number z is a number of the form z=x+iy, x,yER

A: Both the statements are TRUE

Q: By algebraic properties of R, prove that for every x, y € R with y # 0 (-x) y

A: We have to prove that by algebraic property that ∀x,y∈ℝ with y≠0 -xy=-xy

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Q: By expanding both sides of the identity (1+ x)"+4 = (1+x)"(1+x)* prove that ("**) - (") + «(,",) +…

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Q: A sequence (a1, b1), (@2, b2), (a3, b3), -· - - of points in the co- ordinate plane satisfies (am+1;…

A: A sequence a1,b1,a2,b2,a3,b3,... of points in the coordinate plane satisfies the equation…

Q: Find a bijection between the interval (−1, 1) and R.

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