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# De Moivre watch

1. See the picture for Q4.

I got the roots of -4, 1+i, 1-i, -1+i, -1-i

but for the (z-1)4 = -4(z+1)4 I got the roots -1+2i and -1 - 2i but then for the other 2 I got stuck at these points

2(x+ iy) = ix - y + i
and 2(x+iy) = y - ix - i

I'm supposed to get roots 1/5 (-1 +-2y) can someone explain how

thanks
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2. (Original post by bl64)
See the picture for Q4.

I got the roots of -4, 1+i, 1-i, -1+i, -1-i
These are correct.

I'm not sure what you're doing for the second part. Take the fourth root of both sides: and then re-arrange and solve.

One solution: (-4)^(1/4) = 1+i, this gets you , re-arrange and solve for , then rinse and repeat for the other solutions.
3. (Original post by Zacken)
These are correct.

I'm not sure what you're doing for the second part. Take the fourth root of both sides: and then re-arrange and solve.

One solution: (-4)^(1/4) = 1+i, this gets you , re-arrange and solve for , then rinse and repeat for the other solutions.
It's (z-1) = (-4)1/4(z+1) and I did that but only got 2 of the 4 roots
4. (Original post by bl64)
It's (z-1) = (-4)1/4(z+1) and I did that but only got 2 of the 4 roots
Yep, it is. Sorry. What d'you mean you only got two of the solutions? Let's call . Then:

.

Now replace with each of your four roots in turn, does that help?

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