Complex numbers question (1 Viewer)

[cutemouse]

Find the roots of z^4+1=0 and show them in an Argand diagram. Resolve z^4+1 into real quadratic factors. Hence deduce that cos2x=2[cosx-cos(pi/4)][cosx-cos(3pi/4)].


I can do the first bit of sketching it on the Argand diagram...

Thanks.

 

[Tsylana]

The question is strangely odd if its a standalone question, there should have been a question before this that leads to this otherwise the "Hence" part of the question is just... odd..

 

[shaon0]

z^4+1=0 has roots z=cis(+-pi/4), cis(+-3pi/4)
Thus, z^4+1=(z^2-sqrt(2)z+1)(z^2+sqrt(2)z+1)

 

[cutemouse]

Nope, no lead in

 

[untouchablecuz]

 

[shaon0]

Oh crap. Just realised there was another part to the question. lol