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    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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    (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: z + 1 = (-4)^{1/4} (z-1) and then re-arrange and solve.

    One solution: (-4)^(1/4) = 1+i, this gets you z + 1 = (1+i)(z-1), re-arrange and solve for z, then rinse and repeat for the other solutions.
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    (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: z + 1 = (-4)^{1/4} (z-1) and then re-arrange and solve.

    One solution: (-4)^(1/4) = 1+i, this gets you z + 1 = (1+i)(z-1), re-arrange and solve for z, 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
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    (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 (-4)^{1/4} = \alpha. Then:

    \displaystyle z-1 = \pm(\alpha z + \alpha) \Rightarrow z(1\mp \alpha) = 1 \pm \alpha  \Rightarrow z = \frac{1 \pm \alpha}{1\mp \alpha}.

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