Complex Numbers Questions (1 Viewer)

[khfreakau]

It seems I'm a bit rusty... anyone care to jog my memory?

1.a) If z^5 + 1 = 0 and z is a solution, prove 1 + z^2 + z^4 = z + z^3
b) By considering real parts of both sides of part a, show cos(pi/5) + cos (3pi/5) = 1/2

2. Find the locus of z² if Re(z) = 2

That's all for now

 

[jayy100]

ummm, i think this is a roots of unity question :S . so draw it on the argand plane?

 

[ohexploitable]

 

[khfreakau]

Okie doke, seems straightforward enough. (I now remember that factorising method heh). What about the other two?

 

[deterministic]

2. Re(z)=2
So z=2+ib
z^2=4-b^2+4ib
So let X=4-b^2, Y/4=b
so X=4-Y^2/16
Y^2=16(4-X) => Sideways parabola

 

[khfreakau]

Thanks! I was really having trouble with that one.... looks like I really need to revise 4u =/ Last one, anyone?

 

[ohexploitable]

 

[khfreakau]

Thanks heaps buddy!