Question and Answers Forum

All Questions      Topic List

Arithmetic Questions

Previous in All Question      Next in All Question      

Previous in Arithmetic      Next in Arithmetic      

Question Number 68189 by peter frank last updated on 06/Sep/19

Commented by peter frank last updated on 06/Sep/19

Qn 9, 10

$${Qn}\:\mathrm{9},\:\:\mathrm{10} \\ $$

Commented by mind is power last updated on 06/Sep/19

9 ((z_3 −z_1 )/(z_2 −z_1 ))=+−i ⇒(z_3 −z_1 )^2 =−(z_2 −z_1 )^2 ⇒z_3 ^2 −2z_1 z_3 +z_1 ^2 =−z_2 ^2 −z_1 ^2 +2z_2 z_1 ⇒z_3 ^2 +2z_1 ^2 +z_2 ^2 =2(z_1 z_3 +z_1 z_2 )

$$\mathrm{9} \\ $$$$\frac{{z}_{\mathrm{3}} −{z}_{\mathrm{1}} }{{z}_{\mathrm{2}} −{z}_{\mathrm{1}} }=+−{i} \\ $$$$\Rightarrow\left({z}_{\mathrm{3}} −{z}_{\mathrm{1}} \right)^{\mathrm{2}} =−\left({z}_{\mathrm{2}} −{z}_{\mathrm{1}} \right)^{\mathrm{2}} \\ $$$$\Rightarrow{z}_{\mathrm{3}} ^{\mathrm{2}} −\mathrm{2}{z}_{\mathrm{1}} {z}_{\mathrm{3}} +{z}_{\mathrm{1}} ^{\mathrm{2}} =−{z}_{\mathrm{2}} ^{\mathrm{2}} −{z}_{\mathrm{1}} ^{\mathrm{2}} +\mathrm{2}{z}_{\mathrm{2}} {z}_{\mathrm{1}} \\ $$$$\Rightarrow{z}_{\mathrm{3}} ^{\mathrm{2}} +\mathrm{2}{z}_{\mathrm{1}} ^{\mathrm{2}} +{z}_{\mathrm{2}} ^{\mathrm{2}} =\mathrm{2}\left({z}_{\mathrm{1}} {z}_{\mathrm{3}} +{z}_{\mathrm{1}} {z}_{\mathrm{2}} \right) \\ $$

Commented by mind is power last updated on 06/Sep/19

10) us_ e ((z_2 −0)/(z_1 −0))=e^(+_− i(π/3))

$$\left.\mathrm{10}\right)\:{us}_{} {e}\:\frac{{z}_{\mathrm{2}} −\mathrm{0}}{{z}_{\mathrm{1}} −\mathrm{0}}={e}^{\underset{−} {+}{i}\frac{\pi}{\mathrm{3}}} \\ $$

Commented by peter frank last updated on 07/Sep/19

please sir.elaborate and where this ((z_2 −0)/(z_1 −0))=e^(±(π/3)) ?

$${please}\:{sir}.{elaborate}\:{and}\:{where}\:{this}\: \\ $$$$\frac{{z}_{\mathrm{2}} −\mathrm{0}}{{z}_{\mathrm{1}} −\mathrm{0}}={e}^{\pm\frac{\pi}{\mathrm{3}}} \:? \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com