a) Prove that, a dy [r² √а4-y4 4а√2π

Q: The number of integer values of m, for which the x-co- ordinate of the point of intersection of the…

A: Introduction :

Q: 4) Given that z= 3 + 2i and w= √3 - 5i. Find zw and (z/w).

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Q: complex cube roots of -1 are and and hence prove tha 2 1+v? + v3i - V3i = 2 2

A: We have 1+3i23=-11-3i23=-1

Q: Prove the following: If ā and b are in R', then (5 -a)×(5 +a)=-2(āxb).

A: Given a⇀ and b⇀ are in R3. To prove :  b⇀-a⇀×b⇀+a⇀=-2a⇀×b⇀

Q: 4. Which of the following is the quadratic equation? b+b-4ac A) x = -b±b-4ac B) b±yb? -4ac C) x = 2a…

A: This is obtained by sroddhar acharya.

Q: complex numbers Z1= 4.5-j5.1 , Z2= 3.2- 5.2, Z3= 2.25-j5.6 , Z4= 7.5-j9.2 , then alculate…

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Q: Draw a simplicial complex x with seven 1-si- (and possibly simplices to other olimesions), such the…

A: Answer given below in great detail.

Q: 4). Use rules of replacement to prove the following: a). (p^~q) (p^q) = p b). (pvq) →→ r = (p → r) ^…

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Q: 3. Find the positive value of real parts of the possible values of z that satisfy the equation: zz +…

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Q: sider the following quadratic form on R²:

A: Given the quadratic form on R2:                 Q(x)=-4617x12+2917x22+4017x1x2

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: Find all values of a E R such that Q is positive definite, and all values of a E R such that Q is…

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Q: 4. Solve for x : a) V5x +1 = æ + 1 b) a = V3x +7 – 3 c) V2x – 3 – Va – 2 = 1

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Q: The negative complex roots for the quartic equation x* +x² –1=0 are: 1-5 b. i + a. ti 2 c. ti 2 |1+…

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Q: Only solve z for both a) & b) on the attached.

A: To compare two proportions, a hypothesis test can be conducted. If there are ,  are the number of…

Q: 3. If z, and zz are two complex numbers, prove that

A: Let's find.

Q: Prove that there exists a unique real number solution to the equationx +x² – 1 = 0 between x = 2/3…

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Q: 19 a) Edur 1+2r 1 b) (1 +25), | E dr

A: We will solve  the integration.

Q: 4. Calculate Res z+1 z²+9 -3i

A: The answer is (1/2)+(i/6)Explanation:Step 1: Step 2: Step 3: Step 4:

Q: Find the rectangular form of 7T 3√/2e² i.e. the a + bi form. Do not include any spaces.

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Q: 2 7. a) Prove that, So √a-y+= 4a√2¬ dy [r] 0

A: We have to show

Q: Let a and b be complex numbers where a has a non zero imaginary part. a. Show that S = { (a +…

A: Given information:a and b are complex numbers, where a has a non-zero imaginary part.A set S defined…

Q: Verify that z 2 + 4i is a solution of z2 + 6z - 40i = 0. Is 2+ 41 also a solution?

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Q: Ifx.y,z are real numbers satisfying the equation 25(9x + y) +9:*–15(5xy + yz + 3:x)= 0 then prove…

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Q: If w and a² are the nonreal cube roots of unity and [1/(a + c)] + [1/(b + c)] + [1/(c + a)] = 2a²…

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Q: Let a ERR. Prove lal = √a². (note: y = √a² iff y²=a and y=-√a² y = 0)

A: Step 1: Step 2: Step 3: Step 4:

Q: b) Calculate the general solution in implicit form of the equation   c) Find the particular…

A: b. From the given equation, we expand it as follows. For simplified view we will take dydx=y' So…

Q: b) Use an algebraic proof to show that (AUB) - (AUC) = (B-C) - A

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Q: 1. Determine the characteristic of the roots of the quadratic equations. a) х? — х —30 %3D0 b) 7x –…

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Q: 2. Show that a. Q(√5, √-5) = Q(√−1, √5) b. Q(√2, √6) = Q(√2, √3) c. Q(√5, √7) = Q(√5 + √7) d. Q(√a,…

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