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# FP2: Complex numbers (finding the roots) watch

1. I've done the proof part, but I'm not sure how to do the part I've put a box around :/ All I've figured out that there will be 6 roots and theta will equal pi/4
2. (Original post by creativebuzz)

I've done the proof part, but I'm not sure how to do the part I've put a box around :/ All I've figured out that there will be 6 roots and theta will equal pi/4
what about the values of n and theta?
3. (Original post by TeeEm)
what about the values of n and theta?
Yeah I said theta would be pi/4

N would equal 3
4. (Original post by creativebuzz)
Yeah I said theta would be pi/4

N would equal 3
Isn't obvious then that

either

z3 = eiπ/4

or

z3 = e-iπ/4
5. (Original post by TeeEm)
Isn't obvious then that

either

z3 = eiπ/4

or

z3 = e-iπ/4
Maybe it's both
z3 = eiπ/4 AND z3 = e-iπ/4

because you should have 6 roots in the end
6. (Original post by TeeEm)
Isn't obvious then that

either

z3 = eiπ/4

or

z3 = e-iπ/4
I'll try it out, in the meantime, how would you do this question? I can do the represent part, but I can't do the whole "show that |z-4|/|z-1| is a constant" etc
7. (Original post by creativebuzz)
Maybe it's both
z3 = eiπ/4 AND z3 = e-iπ/4

because you should have 6 roots in the end
thank you for letting me know it has 6 roots. Life here is a constant education

(Original post by creativebuzz)
I'll try it out, in the meantime, how would you do this question? I can do the represent part, but I can't do the whole "show that |z-4|/|z-1| is a constant" etc
In the meantime I have to do my own work

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