de moivres theorem (1 Viewer)

[kractus]

im not sure how you would do c given b. I initially thought just base off of inspection that there would be a substitution involving cis or cos theta but its hard for me to tell what to substitute. Or there's just no substirution

 

[member 6003]

i think you substitute z=cistheta and divide by z^3 on both sides. then like using z^n+z^-n=2cosntheta to get the rest of it.

 

[tywebb]

Looks like a cambridge question.

 

[kractus]

Looks like a cambridge question.

View attachment 37522
View attachment 37523
View attachment 37524
View attachment 37525

ya it is cambridhe. I also have another question:

Just iii.

 

[tywebb]

 

[5uckerberg]

View attachment 37521
im not sure how you would do c given b. I initially thought just base off of inspection that there would be a substitution involving cis or cos theta but its hard for me to tell what to substitute. Or there's just no substirution

To start we will first divide with which gives us
With the RHS since you got three multiples a division of is just simply dividing for each quadratic inside the bracket. This in turn will give us

Using our knowledge of conjugates is just .

Take the two out of everyone and multiply it two times it will become 8. This leads to

 

[5uckerberg]

ya it is cambridhe. I also have another question:
View attachment 37526
Just iii.

Help with Cambridge Extension 2 Enrichment Question - Complex Numbers

Hello, I am having trouble doing q a(iii) and b. Could someone help me please? Thanks.

boredofstudies.org

Have a look at this forum.

 

[5uckerberg]

Looks like a cambridge question.

View attachment 37522
View attachment 37523
View attachment 37524
View attachment 37525

Where is the 8 in front of the whole solution?