|z+2i|=|z+1- 3i|

Q: Find two positive real numbers x and y such that they add to 120 and x2y is as large as possible.

A: Oue Aim is to find two positive real nnumbe x and y such that theyadd to 120 and x2y is as large as…

Q: Show that 1 п-1 .. 1 X2 x5 п-1 x2 ... =II("; – 2;) i>j 1 n-1 .. •.

A:

Q: Find all integer x satisfying the condition x = gcd(4x + 3, 2x). Justify your answer.

A: To find all integer x satisfying the condition  x=gcd4x+3,2x

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

A:

Q: z -7 2. prove that: Im(z)= 2i

A:

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

A:

Q: The sum of two positive real numbers x and y is 6. Find an x and y among these such that the product…

A: We need to find x and y.

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

A:

Q: Find two positive real numbers x and y such that they add to 120and x 2y is as large as possible.

A: Given: x+y=120and  y=120-xAlso given that z=x2ybut we have z=x2120-x=120x2-x3    ...(1)

Q: Q1. Prove that for any natural number n, E, 2i = 2n+1 – 1. i%3D0

A: I have used mathematical induction to prove the result

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

A:

Q: (c) Prove that the equation x + 5x = 4cos.x cannot have more than one real root.

A:

Q: Let Let z, = 2-2i ,z, , Z2 =-1-3i find Find 1) 3-i) 2) Arg Z2

A: The complex number is of the form a+bi where a and b are real numbers and i is called iota whose…

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

A:

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…

Q: For all real numbers x, cos (2x)= (a) 2 sin x cos x2 sin x cos x (b) sin (x2)sin x2…

A: SOLUTION- formulaconsider the addition formulacos (A+B)=cos A cos B-sin A sin B

Q: ·C) - G) + G)-G) + +-1 - Prove that for any positive integer n, 0.

A: Use simple property of combination.

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

A:

Q: 1- -1 -1 provethat K K_2I %3D

A:

Q: (a) Prove that the equation –1 = x – x² has a solution in (1, 2). (Do not x +1 attempt to find the…

A: GIVEN11+x-1=x-x2we need to prove the equation

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: 1. The set of all pairs of real numbers of the form (x, 0) with the standard operations on R2.

A: 4. Given that the set of all pairs of real numbers of the form (x, 0) with the standard operation on…

Q: For all real numbers x and y, [x]+ [y] = [x + y] – 1. For all real numbers x, [x –1] = [x] – 1. | -

A:

Q: (2) Find all the numbers z such that elz = 10i.

A: Consider the given. eiz=10i

Q: Find all values of x such that x² 2+ x + 2! = 0. 3! 4! If no such values of x exist, prove this. + +

A:

Q: The sum of two positive real numbers x and y is 3. Find an x and y among these such that the product…

A:

Q: The sum of two positive real numbers x and y is 12. Find an x and y among these such that the…

A: The sum of two positive real numbers x and y is 12.

Q: express z1z2 and (z1/z2) in the form a+ib z1=-1+3i, z2=2-i

A:

Q: Prove that x' +4=(x+1+i)(x+1-i)(x-1+i)(x-1-i).

A:

Q: HW4| Prove How 4 Prove if x;→ × then 6x.→6x Xj ->

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 7. (a) Find all the values of z such that e = 1+ i.

A:

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

A:

Q: Find the sum of f(i) = 2i +2 over the integers 1, 2, 3, ..., 20.

A: Given,           The sum of fi=2i+2 over the integers 1,2,3,...,20

Q: iii) a) Prove that Pa(-x) (-1)".Pn(x) u (2n)! 22 (n!) b) Prove that P2n(0) = (-1)".- %3D

A: To prove- Pn(-x)=(-1)n.Pn(x)P2n(o)=(-1)n.(2n)!22n(n!)2

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

A:

Q: The domain of f(x) = cos-(x) is: O all real numbers [- π/2, π/2] O -1. 1]

A: givenf(x)=cos-1(x)all values of x for which f(x) is valid is called domain.

Q: Let x be a real number. Prove that there is a positive integer n such that the distance between nx…

A: Let x be a real number  To prove there is a positive integer n such that the distanc between nx and…

Q: Find the value of a such that 1 0. 3 2 2 a- 2

A: I have solved the determinant

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

A:

Q: Represent algebraically and graphically the set of values of z for which |z+3|=|z−2i|

A:

Q: 5. The set of all pairs of real numbers of the form (x, y), where x ≥ 0, with the standard…

A:

Q: -2 Find all the values of s €R such that A = -2 -2 is positive definite.

A:

Q: Find the value of k such that A is singular. 0 3 2 -1 0 L 3 3 k k =

A:

Q: Find all values of x in the interval [0,2pi) 2sin^2x+5sinx-3=0

A: Given equation is, 2sin2x+5sin x -3=0

Q: on the closed interval Co,14], (0,14)such that f'ccF FC14D-FCO) 14-0

A: we have to find the value of c

Q: 1. For positive integers i, j,n such that i+ j = n (a) show that corresponding multinomial…

A: sol(a) we know that multinomial co-efficient is definedby ni,j=n!i!,j!  —(1) where i+j=nnow…

Q: Let ß be a positive real number. Evaluate L Bx-1 VxP + 3dx . (50+3 V50+3 - 2ß+3 /20+3 ㅇ 름(5v5-2v2) ㅇ…

A: We use substitution method to solve this integration

Q: (a)] Show that 1+(1+z)/2 csch z In • [(b)] Use part (a) to find all the values of csch (-2i).

A: Let:

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.