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[Further Maths FP2] Roots of unity

Studying nth roots of unity at the moment, and I'm stuck with finding the complex solutions to the following:

16z^4 = (z-1)^4

I get to:

2z = i(z-1)

But don't know where to go from there.

Reply 1

TeeEm

Original post by Haza100

Studying nth roots of unity at the moment, and I'm stuck with finding the complex solutions to the following:

16z^4 = (z-1)^4

I get to:

2z = i(z-1)

But don't know where to go from there.

post your workings are there are more than 1 method for doing this

Reply 2

Haza100

Original post by TeeEm

post your workings are there are more than 1 method for doing this

16z^4 = (z-1)^4

2z = \sqrt[4]{1} (z-1)

\sqrt[4]{1} = 1, -1, i, -i

Solving for real solutions gives z=1/3 and z=-1

Can't seem to rearrange for z to get complex solutions, I must be being stupid... all help appreciated.

Reply 3

TeeEm

Original post by Haza100

16z^4 = (z-1)^4

2z = \sqrt[4]{1} (z-1)

\sqrt[4]{1} = 1, -1, i, -i

Solving for real solutions gives z=1/3 and z=-1

Can't seem to rearrange for z to get complex solutions, I must be being stupid... all help appreciated.