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AlgebraQuestion and Answers: Page 312

Question Number 48272 Answers: 0 Comments: 1

z^5 =32 find all root z

$$\mathrm{z}^{\mathrm{5}} =\mathrm{32} \\ $$$$\mathrm{find}\:\mathrm{all}\:{root}\:{z} \\ $$

Question Number 48225 Answers: 1 Comments: 0

prove that exp(((2+πi)/4))=(√(e/2))(1+i) cos (z_1 +z_2 )=cos z_1 cos z_2 −sin z_1 sin z_2

$$\mathrm{prove}\:\mathrm{that} \\ $$$$\mathrm{exp}\left(\frac{\mathrm{2}+\pi\mathrm{i}}{\mathrm{4}}\right)=\sqrt{\frac{{e}}{\mathrm{2}}}\left(\mathrm{1}+{i}\right) \\ $$$$\mathrm{cos}\:\left({z}_{\mathrm{1}} +{z}_{\mathrm{2}} \right)=\mathrm{cos}\:{z}_{\mathrm{1}} \mathrm{cos}\:{z}_{\mathrm{2}} −\mathrm{sin}\:{z}_{\mathrm{1}} \mathrm{sin}\:{z}_{\mathrm{2}} \\ $$

Question Number 48224 Answers: 1 Comments: 0

e^z =1−(√3)i z=..

$${e}^{{z}} =\mathrm{1}−\sqrt{\mathrm{3}}{i} \\ $$$${z}=.. \\ $$

Question Number 48222 Answers: 0 Comments: 0

f(x)=Σ_(i=0) ^(n) a_i x^i =a_n x^n +a_(n−1) x^(n−1) +a_(n−2) x^(n−2) +…+a_2 x^2 +a_1 x+a_0 f^(−1) (x)=...

$${f}\left({x}\right)=\underset{{i}=\mathrm{0}} {\overset{{n}} {\Sigma}}{a}_{{i}} {x}^{{i}} ={a}_{{n}} {x}^{{n}} +{a}_{{n}−\mathrm{1}} {x}^{{n}−\mathrm{1}} +{a}_{{n}−\mathrm{2}} {x}^{{n}−\mathrm{2}} +\ldots+{a}_{\mathrm{2}} {x}^{\mathrm{2}} +{a}_{\mathrm{1}} {x}+{a}_{\mathrm{0}} \\ $$$${f}^{−\mathrm{1}} \left({x}\right)=... \\ $$

Question Number 48204 Answers: 1 Comments: 0

2(x^4 −2x^2 +3)(y^4 −3y^2 +4)=7 Find (x,y) .

$$\mathrm{2}\left({x}^{\mathrm{4}} −\mathrm{2}{x}^{\mathrm{2}} +\mathrm{3}\right)\left({y}^{\mathrm{4}} −\mathrm{3}{y}^{\mathrm{2}} +\mathrm{4}\right)=\mathrm{7} \\ $$$${Find}\:\left({x},{y}\right)\:. \\ $$

Question Number 48161 Answers: 1 Comments: 1

f(z)=((1−z)/(1+z)) u(x,y)=.. v(x,y)=..

$${f}\left({z}\right)=\frac{\mathrm{1}−{z}}{\mathrm{1}+{z}} \\ $$$${u}\left({x},{y}\right)=.. \\ $$$${v}\left({x},{y}\right)=.. \\ $$$$ \\ $$$$ \\ $$

Question Number 48075 Answers: 1 Comments: 1

solve (∣x^2 −1∣−(1/2))x+((√6)/(18))=0

$$\mathrm{solve}\:\:\:\:\:\left(\mid{x}^{\mathrm{2}} −\mathrm{1}\mid−\frac{\mathrm{1}}{\mathrm{2}}\right){x}+\frac{\sqrt{\mathrm{6}}}{\mathrm{18}}=\mathrm{0} \\ $$

Question Number 48055 Answers: 2 Comments: 6

Solve the system: { ((x^3 +x^2 y−4xy^2 −4y^3 =0)),((x^2 −2xy−3y^2 −x−y=0)) :}

$${Solve}\:{the}\:{system}: \\ $$$$\begin{cases}{{x}^{\mathrm{3}} +{x}^{\mathrm{2}} {y}−\mathrm{4}{xy}^{\mathrm{2}} −\mathrm{4}{y}^{\mathrm{3}} =\mathrm{0}}\\{{x}^{\mathrm{2}} −\mathrm{2}{xy}−\mathrm{3}{y}^{\mathrm{2}} −{x}−{y}=\mathrm{0}}\end{cases} \\ $$

Question Number 47993 Answers: 0 Comments: 5

Solve in R ((59+(√(x−2))))^(1/3) +((12−(√(x−11))))^(1/3) =6

$${Solve}\:{in}\:\mathbb{R} \\ $$$$\sqrt[{\mathrm{3}}]{\mathrm{59}+\sqrt{{x}−\mathrm{2}}}+\sqrt[{\mathrm{3}}]{\mathrm{12}−\sqrt{{x}−\mathrm{11}}}=\mathrm{6} \\ $$

Question Number 47986 Answers: 3 Comments: 1

Question Number 47966 Answers: 1 Comments: 1

a(x^2 +y^2 )+b(x+y)= c & x^2 −y^2 = R^2 Solve for x or y .

$${a}\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right)+{b}\left({x}+{y}\right)=\:{c} \\ $$$$\:\&\:\:\:\:{x}^{\mathrm{2}} −{y}^{\mathrm{2}} \:=\:{R}^{\mathrm{2}} \\ $$$${Solve}\:{for}\:{x}\:{or}\:{y}\:. \\ $$

Question Number 47916 Answers: 2 Comments: 1

Question Number 47807 Answers: 1 Comments: 0

sin xy^2 =y^2 +2x diferential express is

$$\mathrm{sin}\:{xy}^{\mathrm{2}} ={y}^{\mathrm{2}} +\mathrm{2}{x} \\ $$$$ \\ $$$$\mathrm{diferential}\:{express}\:\mathrm{is} \\ $$

Question Number 47778 Answers: 1 Comments: 0

f(x)=2x^3 +x^2 −2x−1 f^(−1) (x)=...

$${f}\left({x}\right)=\mathrm{2}{x}^{\mathrm{3}} +{x}^{\mathrm{2}} −\mathrm{2}{x}−\mathrm{1} \\ $$$${f}^{−\mathrm{1}} \left({x}\right)=... \\ $$

Question Number 47712 Answers: 0 Comments: 0

show that ^(^2 C_2 ) C_n = (1/((1−n)!(n−1)(n−2)(n−3)...3(2)(1)))

$${show}\:{that}\: \\ $$$$\:\:^{\:^{\mathrm{2}} \:{C}_{\mathrm{2}} \:} {C}_{{n}} =\:\frac{\mathrm{1}}{\left(\mathrm{1}−{n}\right)!\left({n}−\mathrm{1}\right)\left({n}−\mathrm{2}\right)\left({n}−\mathrm{3}\right)...\mathrm{3}\left(\mathrm{2}\right)\left(\mathrm{1}\right)} \\ $$

Question Number 47543 Answers: 2 Comments: 0

solve (1+ix)^n =n with x unknown real and n integr natural .

$${solve}\:\left(\mathrm{1}+{ix}\right)^{{n}} ={n}\:\:\:{with}\:{x}\:{unknown}\:{real}\:{and}\:{n}\:{integr}\:{natural}\:. \\ $$

Question Number 47394 Answers: 1 Comments: 1

f(z)=((3z+1)/(2−4z)) f(f(z))=...

$${f}\left({z}\right)=\frac{\mathrm{3}{z}+\mathrm{1}}{\mathrm{2}−\mathrm{4}{z}} \\ $$$${f}\left({f}\left({z}\right)\right)=... \\ $$

Question Number 47391 Answers: 2 Comments: 1

z_1 =3+i z_2 =1−2i determinant ((((2z_2 +z_1 −5−i)/(2z_1 −z_2 +3−i))))^2 =..

$${z}_{\mathrm{1}} =\mathrm{3}+{i} \\ $$$${z}_{\mathrm{2}} =\mathrm{1}−\mathrm{2}{i} \\ $$$$\begin{vmatrix}{\frac{\mathrm{2}{z}_{\mathrm{2}} +{z}_{\mathrm{1}} −\mathrm{5}−{i}}{\mathrm{2}{z}_{\mathrm{1}} −{z}_{\mathrm{2}} +\mathrm{3}−{i}}}\end{vmatrix}^{\mathrm{2}} =.. \\ $$

Question Number 47389 Answers: 0 Comments: 1

((√3)−i)^(1+2i) =...

$$\left(\sqrt{\mathrm{3}}−{i}\right)^{\mathrm{1}+\mathrm{2}{i}} =... \\ $$

Question Number 47331 Answers: 0 Comments: 1

this remained unsolved... ∣x−(3/4)∣×∣x+(5/4)∣=3; x∈C

$$\mathrm{this}\:\mathrm{remained}\:\mathrm{unsolved}... \\ $$$$\mid{x}−\frac{\mathrm{3}}{\mathrm{4}}\mid×\mid{x}+\frac{\mathrm{5}}{\mathrm{4}}\mid=\mathrm{3};\:{x}\in\mathbb{C} \\ $$

Question Number 47291 Answers: 1 Comments: 0

solve for x∈C: ∣x−(3/4)∣×∣x+(5/4)∣=3

$$\mathrm{solve}\:\mathrm{for}\:{x}\in\mathbb{C}: \\ $$$$\mid{x}−\frac{\mathrm{3}}{\mathrm{4}}\mid×\mid{x}+\frac{\mathrm{5}}{\mathrm{4}}\mid=\mathrm{3} \\ $$

Question Number 47239 Answers: 1 Comments: 1

((1.8×10^6 )/(tan(89.9999°))) ∼ π (upto 9 decimal places) can i have some explanations how it is worked out ? Thank you!

$$\frac{\mathrm{1}.\mathrm{8}×\mathrm{10}^{\mathrm{6}} }{{tan}\left(\mathrm{89}.\mathrm{9999}°\right)}\:\sim\:\pi\:\left({upto}\:\mathrm{9}\:{decimal}\:{places}\right) \\ $$$${can}\:{i}\:{have}\:{some}\:{explanations}\:{how}\:{it}\:{is}\:{worked}\:{out}\:? \\ $$$${Thank}\:{you}! \\ $$

Question Number 47139 Answers: 1 Comments: 0

Solve for n: 4^n + 2^n − 6 = (2^n − 4)^3 + (4^n − 2)^3 ....

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{n}:\:\:\:\:\:\:\mathrm{4}^{\mathrm{n}} \:+\:\mathrm{2}^{\mathrm{n}} \:−\:\mathrm{6}\:=\:\left(\mathrm{2}^{\mathrm{n}} \:−\:\mathrm{4}\right)^{\mathrm{3}} \:+\:\left(\mathrm{4}^{\mathrm{n}} \:−\:\mathrm{2}\right)^{\mathrm{3}} \:.... \\ $$

Question Number 47068 Answers: 1 Comments: 0

(a−b)^2

$$\left(\mathrm{a}−\mathrm{b}\right)^{\mathrm{2}} \\ $$

Question Number 47019 Answers: 2 Comments: 2

Question Number 46978 Answers: 2 Comments: 0

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