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Question Number 49174 Answers: 1 Comments: 1

If z_1 ,z_2 and z_3 ,z_(4 ) are two pairs of conjugate complex numbers , then find value of arg((z_1 /z_4 ))+arg((z_2 /z_3 )) ?

$${If}\:{z}_{\mathrm{1}} ,{z}_{\mathrm{2}} \:{and}\:{z}_{\mathrm{3}} ,{z}_{\mathrm{4}\:} {are}\:{two}\:{pairs}\:{of}\: \\ $$$${conjugate}\:{complex}\:{numbers}\:,\:{then}\: \\ $$$${find}\:{value}\:{of}\:{arg}\left(\frac{{z}_{\mathrm{1}} }{{z}_{\mathrm{4}} }\right)+{arg}\left(\frac{{z}_{\mathrm{2}} }{{z}_{\mathrm{3}} }\right)\:? \\ $$

Question Number 49151 Answers: 1 Comments: 0

Let z is complex number satisfying the equation z^2 −(3+i)z+m+2i=0, where mεR. Suppose the equation has a real root, then find the non real root?

$${Let}\:{z}\:{is}\:{complex}\:{number}\:{satisfying} \\ $$$${the}\:{equation}\:{z}^{\mathrm{2}} −\left(\mathrm{3}+{i}\right){z}+{m}+\mathrm{2}{i}=\mathrm{0}, \\ $$$${where}\:{m}\epsilon{R}.\:{Suppose}\:{the}\:{equation} \\ $$$${has}\:{a}\:{real}\:{root},\:{then}\:{find}\:{the}\:{non}\:{real}\:{root}? \\ $$

Question Number 49150 Answers: 0 Comments: 0

F=G((m_1 m_2 )/r^2 ) Explain this formula

$${F}={G}\frac{{m}_{\mathrm{1}} {m}_{\mathrm{2}} }{{r}^{\mathrm{2}} } \\ $$$${Explain}\:{this}\:{formula} \\ $$

Question Number 49148 Answers: 1 Comments: 2

Question Number 49147 Answers: 1 Comments: 0

Question Number 49144 Answers: 0 Comments: 2

∫(1/(x^n +1))dx=??

$$\int\frac{\mathrm{1}}{{x}^{{n}} +\mathrm{1}}{dx}=?? \\ $$

Question Number 49142 Answers: 1 Comments: 0

ln(∞)=?? ln(0)=?? ln(−1)=??

$${ln}\left(\infty\right)=?? \\ $$$${ln}\left(\mathrm{0}\right)=?? \\ $$$${ln}\left(−\mathrm{1}\right)=?? \\ $$

Question Number 49134 Answers: 1 Comments: 0

∫(1/(x^(1/6) +x^(1/3) ))dx=??

$$\int\frac{\mathrm{1}}{{x}^{\mathrm{1}/\mathrm{6}} +{x}^{\mathrm{1}/\mathrm{3}} }{dx}=?? \\ $$

Question Number 49133 Answers: 1 Comments: 1

∫(1/(x^5 +1))dx=??

$$\int\frac{\mathrm{1}}{{x}^{\mathrm{5}} +\mathrm{1}}{dx}=?? \\ $$

Question Number 49130 Answers: 0 Comments: 0

Question Number 49129 Answers: 0 Comments: 1

Question Number 49126 Answers: 1 Comments: 1

prouve it existe 4 intergers a b c and d such n^2 −2 divise a^4 +b^4 +c^4 +d^4

$${prouve}\:{it}\:{existe}\:\mathrm{4}\:{intergers}\:{a}\:{b}\:{c}\:\:{and}\:\:{d}\:{such}\:{n}^{\mathrm{2}} −\mathrm{2}\:\:{divise}\:{a}^{\mathrm{4}} +{b}^{\mathrm{4}} +{c}^{\mathrm{4}} +{d}^{\mathrm{4}} \\ $$

Question Number 49123 Answers: 1 Comments: 1

If a^3 −a−1=0 then find the valueof a^4 +a^3 −a^2 −2a+1

$$\mathrm{If} \\ $$$$\mathrm{a}^{\mathrm{3}} −\mathrm{a}−\mathrm{1}=\mathrm{0} \\ $$$$\mathrm{then}\:\mathrm{find}\:\mathrm{the}\:\mathrm{valueof} \\ $$$$\mathrm{a}^{\mathrm{4}} +\mathrm{a}^{\mathrm{3}} −\mathrm{a}^{\mathrm{2}} −\mathrm{2a}+\mathrm{1} \\ $$

Question Number 49121 Answers: 1 Comments: 0

Question Number 49118 Answers: 1 Comments: 0

Given that the equation 3x^2 +mx+n=0 has roots α + (1/β) and β + (1/(α )) find the value of m and n

$${Given}\:{that}\:{the}\:{equation}\:\:\mathrm{3}{x}^{\mathrm{2}} +{mx}+{n}=\mathrm{0}\:{has}\:{roots}\:\alpha\:+\:\frac{\mathrm{1}}{\beta}\:{and} \\ $$$$\beta\:+\:\frac{\mathrm{1}}{\alpha\:}\:{find}\:{the}\:{value}\:{of}\:\:{m}\:{and}\:{n} \\ $$$$ \\ $$

Question Number 49116 Answers: 1 Comments: 2

Give a proof for : 2 = (√(2 + (√(2 + (√( 2 + (√(2 + (√( 2 ... ))))))))))

$$\mathrm{Give}\:\mathrm{a}\:\mathrm{proof}\:\mathrm{for}\:: \\ $$$$\mathrm{2}\:=\:\sqrt{\mathrm{2}\:+\:\sqrt{\mathrm{2}\:+\:\sqrt{\:\mathrm{2}\:+\:\sqrt{\mathrm{2}\:+\:\sqrt{\:\mathrm{2}\:...\:}}}}} \\ $$

Question Number 49112 Answers: 0 Comments: 1

Question Number 49111 Answers: 1 Comments: 0

Question Number 49101 Answers: 0 Comments: 0

Question Number 49100 Answers: 0 Comments: 0

Question Number 49099 Answers: 0 Comments: 0

Question Number 49097 Answers: 1 Comments: 0

Question Number 49096 Answers: 1 Comments: 0

Question Number 49095 Answers: 1 Comments: 0

prove the existence of n integrs naturals x_1 ,x_2 ,....x_n with x_i ≠x_j for i≠j and (1/x_1 ) +(1/x_2 ) +....+(1/x_n ) =1 .

$${prove}\:{the}\:{existence}\:{of}\:{n}\:{integrs}\:{naturals}\:{x}_{\mathrm{1}} ,{x}_{\mathrm{2}} ,....{x}_{{n}} \:\:\:\:{with}\:{x}_{{i}} \neq{x}_{{j}} {for}\:{i}\neq{j} \\ $$$${and}\:\frac{\mathrm{1}}{{x}_{\mathrm{1}} }\:+\frac{\mathrm{1}}{{x}_{\mathrm{2}} }\:+....+\frac{\mathrm{1}}{{x}_{{n}} }\:=\mathrm{1}\:. \\ $$

Question Number 49094 Answers: 0 Comments: 1

calculate ∫_(−π) ^π (x^2 /(sin(sinx)+(√(1+sin^2 (sinx)))))dx

$${calculate}\:\int_{−\pi} ^{\pi} \:\:\frac{{x}^{\mathrm{2}} }{{sin}\left({sinx}\right)+\sqrt{\mathrm{1}+{sin}^{\mathrm{2}} \left({sinx}\right)}}{dx} \\ $$

Question Number 49093 Answers: 2 Comments: 0

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