(d) Show that 1 + √2 is a unit in R and use this to conclude that R has infinitely many units. (e) Determine if 3 - √2 and 5+ 4√2 are associate in R.

Q: -7x Sre™-3 + x + x = 1 dx The 3x لوکی

A: Topic:- application of integration

Q: Show that if |z1| ≤ 2 and |z2| ≤ 3, then one has |(3+4i) 2₁ (1 + i)21 22 ≤ 10+6√2 21 -

A:

Q: Find the argument of 1+i ал with integer a,b b write your answer as a/b for Arg (1+i) =-

A: We have to find the argument of 1+i in the form of arg(1+i)=aπb with integer a, b.

Q: Let a and b be integers so that (a, b) = 1. Prove that (a + b, a – b) divides 2.

A:

Q: 2 in Express (2 + √2₁) simplest a + bi form.

A:

Q: how the element 2+√3 has a multiplicative inverse in Q(√3). Show that Q(√3) is a subfield of C

A:

Q: 3 S ₁² √ (²√₁² - ²√+²) ³ dt

A: Given

Q: Show that if x is an integer, then gcd(x + 1, x2 – x + 1) divides 3. -

A: First, we find gcdx+1, x2-x+1 Now, factors of x+1 are x+1, 1 x2-x+1 is a quadratic equation of the…

Q: Solve for x x2-x-6 2x+12 x-6 2x

A:

Q: - - Do the polynomials t³ + t +2, t² − t +2, t³ +2, and −t³ + t² − 5t +3 - span P3? (Give support…

A:

Q: Find a counterexample to show that each conjecture is false. The difference of two integers is less…

A: To prove the given conjecture false.

Q: If n = 12 m (me N), prove that "C₂ (2+√3)² "Co- - + "C4 (2+√√3)4 n "C6 (2+√3)6 ·+···=(-

A:

Q: Which of the following is equal to 1-√3|? 01-√3 O√3-1 O (1-√3)² O√2 O√

A:

Q: 1. If a = 37 – 43 + k 2a - 36 a) 2 and 6 = -27+33 - k 7 b) a +56 express each of the following terms…

A:

Q: 1) Name the polynomial a) 3x? + 9x - 1 b) 2x* - 9x? - 1

A: a) 3x2+9x-1The above polynomial has a degree 2⇒It is quadratic polynomial