Factor each of 17, 53, and 19i-13 into a product of Gaussian
primes. Find the gcd...
Factor each of 17, 53, and 19i-13 into a product of Gaussian
primes. Find the gcd of each pair from the factorization.
Consider the ring R = Z∞ = {(a1,a2,a3,···) : ai ∈ Z for all
i}.
It...
Consider the ring R = Z∞ = {(a1,a2,a3,···) : ai ∈ Z for all
i}.
It turns out that R forms a ring under the operations:
(a1,a2,a3,···)+(b1,b2,b3,···)=(a1 +b1,a2 +b2,a3 +b3,···),
(a1,a2,a3,···)·(b1,b2,b3,···)=(a1 ·b1,a2 ·b2,a3 ·b3,···)
Let I = {(a1,a2,a3,···) ∈ Z∞ : all but finitely many ai are 0}.
You may use without proof the fact that I forms an ideal of R.
a) Is I principal in R? Prove your claim.
b) Is I prime in R? Prove your claim....
Consider the ring R = Z∞ = {(a1,a2,a3,···) : ai ∈ Z for all
i}.
It...
Consider the ring R = Z∞ = {(a1,a2,a3,···) : ai ∈ Z for all
i}.
It turns out that R forms a ring under the operations:
(a1,a2,a3,···)+(b1,b2,b3,···)=(a1 +b1,a2 +b2,a3 +b3,···),
(a1,a2,a3,···)·(b1,b2,b3,···)=(a1 ·b1,a2 ·b2,a3 ·b3,···)
Let I = {(a1,a2,a3,···) ∈ Z∞ : all but finitely many ai are 0}.
You may use without proof the fact that I forms an ideal of R.
a) Is I principal in R? Prove your claim.
b) Is I prime in R? Prove your claim....
Given P(x)=3x^5−x^4+88x^3−48x^2−720x−432, and that 6i is a zero,
write P in factored form (as a product...
Given P(x)=3x^5−x^4+88x^3−48x^2−720x−432, and that 6i is a zero,
write P in factored form (as a product of linear factors). Be sure
to write the full equation, including P(x)=
Given P(x)=3x^5−x^4+88x^3−48x^2−720^x−432, and that 6i is a
zero, write P in factored form (as a product...
Given P(x)=3x^5−x^4+88x^3−48x^2−720^x−432, and that 6i is a
zero, write P in factored form (as a product of linear factors). Be
sure to write the full equation, including P(x)=
1.
a) Draw a sketch of: {z∈C|Im((3−2i)z)>6}.
b) If 2i is a zero of p(z)=az^2+z^3+bz+16, find...
1.
a) Draw a sketch of: {z∈C|Im((3−2i)z)>6}.
b) If 2i is a zero of p(z)=az^2+z^3+bz+16, find the real
numbers a,b.
c) Let p(z)=z^4−z^3−2z^2+a+6z, where a is real. Given that 1+i
is a zero of p(z):
Find value of a, and a real quadratic factor of p(z). Express
p(z)as a product of two real quadratic factors to find all four
zeros of p(z).
the monthly income I, in dollars, from a new product is given
by
I(t) = 8900...
the monthly income I, in dollars, from a new product is given
by
I(t) = 8900 - 6500e-0.007t
where t is the time, in months, since the product was first
put on the market.
(a) What was the monthly income after the 10th month and
after the 100th month? Round to nearest cent.
(b) What will the monthly income from the product appraoch
as the time increases without bound?
Which elements of Z[i] can be factored non-trivially? Explicitly
factor out those that can be factored...
Which elements of Z[i] can be factored non-trivially? Explicitly
factor out those that can be factored out non-trivially. 3i, 5i, 2
+ i, 3 + i, 2, 3, 5, 7, 11, 13, 15. What conjecture can be made
about which Gaussian integers can be factored non-trivially?