Use z =a +bi and w = c+di to show that z +w=z+W. To show that z + w =z+w, start with the left side. z+w = a+bi +| Substitute z and w.

Q: Prove that: m3 = m – 3m,m, + 2m²

A: Hello! As you have posted 2 different questions, we are answering the first question. In case you…

Q: Assume that u - v = 2, ||u|| = 8, and ||v|| = 3. Calculate the value of (9u + v) · (u – 8v). %3D…

A: we multiply the given equation and then put the value of given data. u=8 v=3 u.v =2 note- According…

Q: the basis of P2 cons tive to B.

A: Introduction: For some n, consider V to be a subspace of Rn. A basis for V is a collection of…

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: Say that E = Ãek™, where the components of A and k are real and constant, i.e. they aren't imaginary…

A: A vector is a quantity that has both magnitude and direction. In general, vectors are represented as…

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: Use z = a + bi and w = c + di to show that z + w =7 + W.

A: Consider a complex number z=a+bi Then, the complex conjugate of above complex number is given by:…

Q: Use the given LU factorization to find all solutions to Ax = b 0 5 1 0 0 15 A = 4 1 0 0 -2 |, b 54…

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Q: 2. If BDbisects <ABCand m<ABD=10x-3 and m<DBC=2x+5, find m<ABC. A

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Q: Verify that v2+ V5 is algebraic over Q.

A: Algebraic number :- An algebraic number is a number that is a root of a non-zero polynomial in one…

Q: 1-Show that У +їх ave X + iy =/=1 where Complex numbers ? X+iy and

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Q: Prove in detail that Q(/3+ v7) = Q(V3, v7) %3D

A: According to guidelines we solve one question.

Q: How did they calculate what T does to the elements of B?

A: You want to know "How did they calculate what T does to the elements of B?" We have  B=1, x, x2, x3…

Q: Prove that the equation ! + = 1 has no solutions in positive integers æ, y, z.

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Q: 3. Show that (1+i) = 2i

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Q: HW/ IF 2, = 1-3i, Zz=-2+si & Z3 = -3-4i determine as a+bi ,0 .0 z,-2.. 2;

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

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 &amp;   (1-i)6

Q: Given that 32a × 11º = 274x × 332× express a in terms of x?

A: Find your answer below

Q: Solve the following IBVP: 0 0, u(x,0) = 2 – 2x2, u(x,0) = 0, 0 0, %3D %3!

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Q: ez = -2

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Q: Prove that ifx > 3 and y> 4, then xy > 11.

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Q: is bijection. Do the same thing with Z,.

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Q: Use z = a + bị to show that z + 7 = 2a and z - 7 = 2bi.

A: Given: z=a+ib

Q: Suppose z = a+ bi, w = u + iv, and

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Q: Prove that the equation x+5x=4cosx cannot have more than one real ro

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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: let (X, Z) %3. üit piece wise comnected ?

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Q: If z1:2., are complex numbers such that =|= =. = |=,| =1, Prove that

A: To prove: z1+z2+…+zn=1z1+1z2+…+1zn Given: z1=z2=…=zn=1 Since, (1) zz¯=|z|2 (2) z=z¯

Q: PROVE that 2a + b = 0.

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Q: If Z1 = 4 + 5i and Z 2 = -1 + I,  express in the form a + bi  (i) Z1 + Z2   (ii) Z1 – Z2

A: Formula used  sum of two complex number is given by  (a1+b1i)+(a2+b2i)=(a1+a2)+i(b1+b2)

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

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

A: Answer

Q: (i) find gcd(2,3+5i) in Z[i], (ii) show that 3+4i and 4-3i are associates in Z[i] , do all , dont…

A: Solution (i)

Q: show that x'-15x +C= O has at most root on E2,2] one

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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: Prove that jer² √ d dx = 2

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Q: 8. What is v–121+ 15 in the form a + bi? 0 + 4i 0 – 26i 15 – 11i O 15 + 11i

A: In complex number, a+ib, a is a real part and b is a imaginary part. We can write,…

Q: See picture

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Q: If z = a+bi for some real numbers a and b, show that |2| = |5|.

A: In the regular geometry on R3, we can compute the distance between                 x,y∈R2 and the…

Q: If z = 1 - 2j and w= 2 - 3j, express 2. w in the form a + bj where a and b are real.

A: Given  z=1−2jw=2−3j

Q: Use the following problem: Given that Z1= Z4, prove that 22 = 23. 3 Write your proof (in any…

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

A: The given value of z is z=3-3i.

Q: Prove that for а + —1,а > 0, пENis (1+ а)" > 1+ па.

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Q: Use the given LU factorization to find all solutions to Ax = b -7 4 9 |,b : 1 0 01 -7 1 0 -1 7 1 -39…

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Q: Construct two bijections from (0,1) to (1,1/0).

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Q: Use z = a + bi to show that z + -z = 2a and z - -z = 2bi.

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Q: 4. Show that: do Tb/(a? – b²) - a+bcos0 а b2 Where a>b>0 such that * -1+ 1. < 1 - a²

A: To Show: ∫0πdθa+bcosθ=πba2-b2 Concept: i. 1+tan2x=sec2xii. cos x=1-tan2x21+tan2x2iii.…

Q: Suppose that B is a point between A and C. Prove that AB−→ =AC−→

A: B is a point on AC. Let, A=(x1,y1) and C=(x3,y3)Then direction vector of AC=(x3 - x1, y3-y1)

Q: 19. Express in a + bi form: (5 – 6yi)(4 + 8i) – [(2 – 3yi) – 3(1+ 6i)]

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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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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.