z = (a + bi)4n+ (b + ai) 4n; a ∈ ℝ ; b ∈ ℝ; n ∈ ℕ. Show that z is a real number.

Q: If x is any positive integer , then the sum of 6x and 11x is always divisible by what?

A: x is a positive integer. Find sum of 6x and 11x is divisible by what?

Q: 10. Show that the product of a+bi and b+ai always results in a purely imaginary number, given that a…

A: Given two complex numbers: a+bi and b+ai

Q: {X = I (mod 3) 2X= 2 (mod 5)

A:

Q: Prove that the last two digits of 2" cannot be 02 and the last three digits cannot be 108.

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

Q: Discrete

A:

Q: Prove: If a > 0, then (1/a) > 0.

A: It is given that a> 0.It is known that if ab > 0 then a > 0 or b > 0 or a< 0 or b…

Q: Prove that if x is a real number, then ⌊2x⌋ = ⌊x⌋ + ⌊x + 1/2 ⌋.

A:

Q: Outline a proof of the theorem by contradiction

A: On considering the theorem If A and B are comingled matrices then the product AB is commingled…

Q: Show that the set of a+bi : a€Z, b€Z, i=root of (-1) Gaussian integers has the same strength as the…

A: ANSWER :

Q: Prove that a perfect square must be of the form 5n or 5n ± 1.

A:

Q: (b) Show that įn is real, even though i or 9i is not.

A:

Q: Let c, a, B be nonzero real numbers such that c + B. Find a given that 202n–3 19 cn 4 ac2 n-3 C - B

A:

Q: prove that :: 2) (1+i) (1-1)² = 64

A:

Q: Prove that (A-1)-1 = A. %3|

A: Let A be inverse of matrix A. Then, by definition We know that

Q: Prove that V3 is irrational

A:

Q: The set of all numbers in the form a + bi is called the set of_______ numbers. If b ≠ 0, then the…

A:

Q: By using Caushy Rieman prove that (2) and (3) (2) 4c2) = (3) prove That (3)- 3.

A:

Q: Let a be a real number. Prove by contrapositive that if a+ 7x = 90, then a < 4.

A:

Q: Prove that if a > 0, and b is an arbitrary real number then x³ + ax + b= 0 has exactly ne real…

A:

Q: Given that 22 = Z4, prove that Zl= 23. 1/2 3 st at least three facts you may use to complete this…

A:

Q: Prove that v5 is irrational.

A: To prove 5 is irrational. Use the method of proof by contradiction.

Q: Prove by contradiction that if 3x? 2 is irrational then r is irrational.

A: We have to show that x is irrational if 3x2-25 is irrational. We have to prove the statement by…

Q: prove that √2+√3 is irrational

A: For rational we needed form p by q P and q are integer

Q: Prove that V2 is irrational.

A: We will prove by the method of contradiction. We will first assume the number to be rational and…

Q: Show that if u is an odd integer ,then the equation x2 +x−u=0 has no solution that is an integer.

A: The objective is to prove that x2+x-u=0 has no solution that is an integer. Suppose that there…

Q: if z1-z2 and z1/z2 are both real then prove that two must either real or equal to each other

A: Suppose z1-z2 and z1z2 are both real. We need to prove either z1 and z2 are real or equal to each…

Q: prove that 3^1/2 is irrational

A: We have to prove that 3^1/2 is an irrational number.Let us assume that 3^1/2 is a rational number.…

Q: Prove that Co +2C, +4C₂ +8C3 +..... +2 °C₁ = 3^

A: Given problem:- Prove that C0 +2C1+4C2+8C3+...... + 2n nCn =3n

Q: Let c, a, ß be nonzero real numbers such that c + B. Find a given that 52n-3 ac2 17 cn–4 n=3 с — в O…

A: According to question given that ∑n=3∞1752n-3cn-4=αc2c-β

Q: Prove that the roots of ax+4=2x²-bx are real for all values of a and b

A: The nature of roots of a quadratic equation Ax2+Bx+C=0  is:

Q: Prove that if x is a real number, then [2x] = [x] +

A:

Q: If x and y are real numbers and x>1, prove that there exists a positive integer n such that x" > y

A:

Q: Prove that (3+2/5) is irrational

A:

Q: Let a be a positive real number and I = , Sdydx. 1 2vx

A:

Q: If a, b, c are integer powers of 2, prove that equation a° + 64 .3 + 64 = c5

A: Given: Let's take a,b,c are integer powers of 2. Prove that a3+b4 =c5  does not have a solution.

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: Prove that √2 is not an element of Q(?).

A:

Q: Prove that 2+/3 is irrational

A: Given,          To Prove : 2+3 is irrational.

Q: . Prove that V6 is irrational number. -. If a, b e R, prove that ab <(a² + b°).

A: We have to prove that 6 is irrational number

Q: b. Prove that 2 is irrational.

A:

Q: Prove that if a, 6, and c are positive real numbers with ab = c, then a < yc or 6 < Vc.

A:

Q: Prove that if x is real number then L2xd =LxJe bx+!]

A: We will prove the expression by two  steps taking real number x in two form.

Q: Let c, a, ß be nonzero real numbers such that c + B. Find a given that 52n-3 19 cn-4 ac² с — В n=3 O…

A:

Q: Prove that 1.9 = 2.

A: To prove: 1.9=2

Q: Prove that ifx^2−6x+ 3is odd, then x is even

A:

Q: Suppose x is a real number and x + 0. Prove that if then x 7 8. 2 16

A:

Q: Let z and y be real numbers. Prove that, if 5æ + y > 11, then z> 2 or y > 1.

A:

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.