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# Difficult FP1 complex numbers question

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1. What I've tried:

- Attempting to repeatedly expand . When , the result is -1.

- Realized that must be a multiple of 4

Anything else I can do? I don't have much experience with proofs so I'm not entirely sure how to move on

What I've tried:

- Attempting to repeatedly expand . When , the result is -1.

- Realized that must be a multiple of 4

Anything else I can do? I don't have much experience with proofs so I'm not entirely sure how to move on
If you write it in exponential form .
3. (Original post by B_9710)
If you write it in exponential form .
Thanks for the reply. I haven't come across that type of maths so far - only FP1's complex numbers. Could you perhaps elaborate on how I could use that fact towards a solution?
4. you can use (a^b)^c = a(b*c) for z_1 and z_2, sub into the constraint equation, and then take logs and solve for k.
Note that when you multiply 2 complex numbers , you get a new complex number whose:

1) length is the products of
2) angle is the sum of the angles of

Here, so taking integer powers of these numbers doesn't change their lengths.

Also:

so

Now you require that these complex number powers are equal; that means that their lengths must be the same (which they are, so forget this) and that they have the same angle, up to a multiple of 360. So we require that the angles differ by a multiple of 360 i.e. we need:

for some

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