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Question Number 49294 Answers: 1 Comments: 0

Question Number 49283 Answers: 1 Comments: 0

Question Number 49280 Answers: 1 Comments: 3

Question Number 49272 Answers: 2 Comments: 0

ZεC satisfies the condition ∣Z∣≥3. Then find the least value of ∣Z+(1/Z)∣ ?

$${Z}\epsilon\mathbb{C}\:{satisfies}\:{the}\:{condition}\:\mid{Z}\mid\geqslant\mathrm{3}. \\ $$$${Then}\:{find}\:{the}\:{least}\:{value}\:{of}\:\mid{Z}+\frac{\mathrm{1}}{{Z}}\mid\:? \\ $$

Question Number 49279 Answers: 2 Comments: 1

Question Number 49256 Answers: 2 Comments: 0

Question Number 49253 Answers: 2 Comments: 0

Question Number 49252 Answers: 1 Comments: 0

Question Number 49251 Answers: 5 Comments: 1

Question Number 49250 Answers: 1 Comments: 0

Apply derivative criteria F(x)=x^3 +5x^2 −2x+3

$${Apply}\:{derivative}\:{criteria} \\ $$$${F}\left({x}\right)={x}^{\mathrm{3}} +\mathrm{5}{x}^{\mathrm{2}} −\mathrm{2}{x}+\mathrm{3} \\ $$

Question Number 49248 Answers: 1 Comments: 0

1) solve z^4 =1+i(√3) 2) factorize p(x)=x^4 −1−i(√3)inside C[x] 3)factorze inside R[x] the polynom p(x).

$$\left.\mathrm{1}\right)\:{solve}\:{z}^{\mathrm{4}} =\mathrm{1}+{i}\sqrt{\mathrm{3}} \\ $$$$\left.\mathrm{2}\right)\:{factorize}\:{p}\left({x}\right)={x}^{\mathrm{4}} −\mathrm{1}−{i}\sqrt{\mathrm{3}}{inside}\:{C}\left[{x}\right] \\ $$$$\left.\mathrm{3}\right){factorze}\:{inside}\:{R}\left[{x}\right]\:{the}\:{polynom}\:{p}\left({x}\right). \\ $$

Question Number 49244 Answers: 1 Comments: 0

let w from C and w^n =1 find the value of S =Σ_(k=0) ^(n−1) C_n ^k w^k .

$${let}\:{w}\:{from}\:{C}\:{and}\:{w}^{{n}} \:=\mathrm{1}\:{find}\:{the}\:{value}\:{of}\: \\ $$$${S}\:=\sum_{{k}=\mathrm{0}} ^{{n}−\mathrm{1}} \:{C}_{{n}} ^{{k}} \:{w}^{{k}} \:. \\ $$

Question Number 49246 Answers: 0 Comments: 0

simplify Π_(k=0) ^(n−1) (e^(i((4kπ)/n)) −2cosθ e^((i2π)/n) +1)

$${simplify}\:\:\:\prod_{{k}=\mathrm{0}} ^{{n}−\mathrm{1}} \left({e}^{{i}\frac{\mathrm{4}{k}\pi}{{n}}} \:−\mathrm{2}{cos}\theta\:{e}^{\frac{{i}\mathrm{2}\pi}{{n}}} \:+\mathrm{1}\right) \\ $$

Question Number 49245 Answers: 0 Comments: 0

solve inside C: 1+(z−1)^3 +(z−1)^6 =0

$${solve}\:{inside}\:{C}:\:\mathrm{1}+\left({z}−\mathrm{1}\right)^{\mathrm{3}} \:+\left({z}−\mathrm{1}\right)^{\mathrm{6}} =\mathrm{0} \\ $$

Question Number 49242 Answers: 0 Comments: 0

let z from C and θ from R and z^2 +2zcosθ +1 =0 find the value of z^(2n) +2zcos(nθ)+1 .

$${let}\:{z}\:{from}\:{C}\:{and}\:\theta\:{from}\:{R}\:{and}\:{z}^{\mathrm{2}} \:+\mathrm{2}{zcos}\theta\:+\mathrm{1}\:=\mathrm{0}\:{find}\:{the}\:{value}\:{of} \\ $$$${z}^{\mathrm{2}{n}} \:+\mathrm{2}{zcos}\left({n}\theta\right)+\mathrm{1}\:. \\ $$$$ \\ $$

Question Number 49241 Answers: 0 Comments: 0

let z =r e^(iθ) find the value of P_n =(z+z^− )(z^2 +z^−^2 ).....(z^n +z^−^n ) .

$${let}\:{z}\:={r}\:{e}^{{i}\theta} \:\:\:{find}\:{the}\:{value}\:{of}\: \\ $$$${P}_{{n}} =\left({z}+\overset{−} {{z}}\right)\left({z}^{\mathrm{2}} \:+\overset{−^{\mathrm{2}} } {{z}}\right).....\left({z}^{{n}} \:+\overset{−^{{n}} } {{z}}\right)\:. \\ $$

Question Number 49249 Answers: 0 Comments: 0

smplify A_(np) =Σ_(k=0) ^(n−1) cos(pk) and B_(np) =Σ_(k=0) ^(n−1) sin(pk) with p fromN

$${smplify}\:{A}_{{np}} =\sum_{{k}=\mathrm{0}} ^{{n}−\mathrm{1}} \:{cos}\left({pk}\right)\:\:{and}\:{B}_{{np}} \:=\sum_{{k}=\mathrm{0}} ^{{n}−\mathrm{1}} \:{sin}\left({pk}\right)\:{with}\:{p}\:{fromN} \\ $$

Question Number 49238 Answers: 0 Comments: 3

Find the maximum common divisor of the folllwing polynomials: •f(x)=x^4 +5x^3 −4x^2 −2x and g(x)=−3x^4 −x^3 +4x^2 in Q[x]. •f(x)=2x^2 −2 and g(x)=x^4 −3x^3 +x^2 +3x−2 in R[x]

$${Find}\:{the}\:{maximum}\:{common}\:{divisor} \\ $$$${of}\:{the}\:{folllwing}\:{polynomials}: \\ $$$$\bullet{f}\left({x}\right)={x}^{\mathrm{4}} +\mathrm{5}{x}^{\mathrm{3}} −\mathrm{4}{x}^{\mathrm{2}} −\mathrm{2}{x}\:{and}\: \\ $$$${g}\left({x}\right)=−\mathrm{3}{x}^{\mathrm{4}} −{x}^{\mathrm{3}} +\mathrm{4}{x}^{\mathrm{2}} \:{in}\:{Q}\left[{x}\right]. \\ $$$$\bullet{f}\left({x}\right)=\mathrm{2}{x}^{\mathrm{2}} −\mathrm{2}\:{and}\:{g}\left({x}\right)={x}^{\mathrm{4}} −\mathrm{3}{x}^{\mathrm{3}} +{x}^{\mathrm{2}} +\mathrm{3}{x}−\mathrm{2}\:{in}\:{R}\left[{x}\right] \\ $$

Question Number 49237 Answers: 0 Comments: 0

Find a polynomial f(x)∈Q[x] such that its main coefficient is 1 and ((√2)+(√3))∈V(f)

$${Find}\:{a}\:{polynomial}\:{f}\left({x}\right)\in{Q}\left[{x}\right]\:{such} \\ $$$${that}\:{its}\:{main}\:{coefficient}\:{is}\:\mathrm{1}\:{and}\: \\ $$$$\left(\sqrt{\mathrm{2}}+\sqrt{\mathrm{3}}\right)\in{V}\left({f}\right) \\ $$

Question Number 49236 Answers: 0 Comments: 2

Let K be a field and a,b∈K. Show that (x−a)(x−b) if and only if a=b

$${Let}\:{K}\:{be}\:{a}\:{field}\:{and}\:{a},{b}\in{K}.\:{Show}\: \\ $$$${that}\:\left({x}−{a}\right)\left({x}−{b}\right)\:{if}\:{and}\:{only}\:{if}\:{a}={b} \\ $$

Question Number 49235 Answers: 0 Comments: 0

Let A a conmutative ring with 1 (not necessarily a whole domain). Study the structure that has A(x) with the usual operations Is it a ring always? Is it a whole domain? How are the units?

$${Let}\:{A}\:{a}\:{conmutative}\:{ring}\:{with}\:\mathrm{1}\: \\ $$$$\left({not}\:{necessarily}\:{a}\:{whole}\:{domain}\right). \\ $$$${Study}\:{the}\:{structure}\:{that}\:{has}\:{A}\left({x}\right)\: \\ $$$${with}\:{the}\:{usual}\:{operations} \\ $$$${Is}\:{it}\:{a}\:{ring}\:{always}? \\ $$$${Is}\:{it}\:{a}\:{whole}\:{domain}? \\ $$$${How}\:{are}\:{the}\:{units}? \\ $$

Question Number 49232 Answers: 0 Comments: 2

let f(a)= ∫_(−∞) ^(+∞) cos(x^2 +ax +1)dx 1)calculate f(a) and f^′ (a) 2) find f^((n)) (a)

$${let}\:{f}\left({a}\right)=\:\int_{−\infty} ^{+\infty} {cos}\left({x}^{\mathrm{2}} \:+{ax}\:+\mathrm{1}\right){dx} \\ $$$$\left.\mathrm{1}\right){calculate}\:{f}\left({a}\right)\:{and}\:{f}^{'} \left({a}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:\:{f}^{\left({n}\right)} \left({a}\right)\: \\ $$

Question Number 49230 Answers: 0 Comments: 0

Question Number 49229 Answers: 0 Comments: 4

x^2 −y^2

$$\boldsymbol{{x}}^{\mathrm{2}} −\boldsymbol{{y}}^{\mathrm{2}} \\ $$

Question Number 49225 Answers: 1 Comments: 0

∫(1/(z(z^(17) +1)))=?? find please

$$\int\frac{\mathrm{1}}{{z}\left({z}^{\mathrm{17}} +\mathrm{1}\right)}=??\:{find}\:{please} \\ $$

Question Number 49222 Answers: 0 Comments: 0

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