Question and Answers Forum

All Questions      Topic List

Others Questions

Previous in All Question      Next in All Question      

Previous in Others      Next in Others      

Question Number 183667 by Mastermind last updated on 28/Dec/22

If w is one of the complex cube   roots of unity, show that  (a+wb+w^2 c)(a+w^2 b+wc) is equal  to (α^2 +b^2 +c^2 −ab−bc−cα).      Kindly help me out, Thank you.

$$\mathrm{If}\:\mathrm{w}\:\mathrm{is}\:\mathrm{one}\:\mathrm{of}\:\mathrm{the}\:\mathrm{complex}\:\mathrm{cube}\: \\ $$$$\mathrm{roots}\:\mathrm{of}\:\mathrm{unity},\:\mathrm{show}\:\mathrm{that} \\ $$$$\left(\mathrm{a}+\mathrm{wb}+\mathrm{w}^{\mathrm{2}} \mathrm{c}\right)\left(\mathrm{a}+\mathrm{w}^{\mathrm{2}} \mathrm{b}+\mathrm{wc}\right)\:\mathrm{is}\:\mathrm{equal} \\ $$$$\mathrm{to}\:\left(\alpha^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}} +\mathrm{c}^{\mathrm{2}} −\mathrm{ab}−\mathrm{bc}−\mathrm{c}\alpha\right). \\ $$$$ \\ $$$$ \\ $$$$\mathrm{Kindly}\:\mathrm{help}\:\mathrm{me}\:\mathrm{out},\:\mathrm{Thank}\:\mathrm{you}. \\ $$

Commented by mr W last updated on 28/Dec/22

if you know (a+b)(c+d), then you can  also solve this.

$${if}\:{you}\:{know}\:\left({a}+{b}\right)\left({c}+{d}\right),\:{then}\:{you}\:{can} \\ $$$${also}\:{solve}\:{this}. \\ $$

Commented by Frix last updated on 28/Dec/22

w^2 =conj w ⇒ w^2 +w=−1  w^3 =1  Should be easy now.

$${w}^{\mathrm{2}} =\mathrm{conj}\:{w}\:\Rightarrow\:{w}^{\mathrm{2}} +{w}=−\mathrm{1} \\ $$$${w}^{\mathrm{3}} =\mathrm{1} \\ $$$$\mathrm{Should}\:\mathrm{be}\:\mathrm{easy}\:\mathrm{now}. \\ $$

Commented by Rasheed.Sindhi last updated on 28/Dec/22

Typos in your question as usual.  Corrected version:  (a+ωb+ω^2 c)(a+ω^2 b+ωc)                =a^2 +b^2 +c^2 −ab−bc−ca

$$\mathcal{T}{ypos}\:{in}\:{your}\:{question}\:{as}\:{usual}. \\ $$$${Corrected}\:{version}: \\ $$$$\left(\mathrm{a}+\omega\mathrm{b}+\omega^{\mathrm{2}} \mathrm{c}\right)\left(\mathrm{a}+\omega^{\mathrm{2}} \mathrm{b}+\omega\mathrm{c}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\mathrm{a}^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}} +\mathrm{c}^{\mathrm{2}} −\mathrm{ab}−\mathrm{bc}−\mathrm{ca} \\ $$

Commented by Mastermind last updated on 28/Dec/22

Thank you sir   but i can′t see the solution

$$\mathrm{Thank}\:\mathrm{you}\:\mathrm{sir}\: \\ $$$$\mathrm{but}\:\mathrm{i}\:\mathrm{can}'\mathrm{t}\:\mathrm{see}\:\mathrm{the}\:\mathrm{solution} \\ $$

Commented by Frix last updated on 28/Dec/22

Maybe the Master of the Mind is not the  Master of the Formulas?

$$\mathrm{Maybe}\:\mathrm{the}\:\mathrm{Master}\:\mathrm{of}\:\mathrm{the}\:\mathrm{Mind}\:\mathrm{is}\:\mathrm{not}\:\mathrm{the} \\ $$$$\mathrm{Master}\:\mathrm{of}\:\mathrm{the}\:\mathrm{Formulas}? \\ $$

Commented by Rasheed.Sindhi last updated on 10/Jan/23

✌️ Share your solution then

Commented by Mastermind last updated on 10/Jan/23

Smile   Anyways, have gotten it BOSS

$$\mathrm{Smile}\: \\ $$$$\mathrm{Anyways},\:\mathrm{have}\:\mathrm{gotten}\:\mathrm{it}\:\mathrm{BOSS} \\ $$

Commented by Mastermind last updated on 19/Jan/23

Terms of Service

Privacy Policy

Contact: info@tinkutara.com