Expert: Ahmed Salami - 10/22/2004

Question
(z-1) power 5=(z+1)power 5    Z=?

Answer
Hi Mariam,
(z-1)^5 = (z+1)^5
Expanding both sides gives
z^5 - 5z^4 + 10z^3 - 10z^2 + 5z - 1   
= z^5 + 5z^4 + 10z^3 + 10z^2 + 5z + 1
Therefore,
10z^4 + 20z^2 + 2 = 0
This is a quadratic equation in z^2 i.e we could say k = z^2 and get
10k^2 + 20k + 2 = 0
which gives
k = [-20 +or- sqrt(20^2 - 4.10.2)]/2.10
 = [-20 +or- sqrt(320)]/20
 = -1 +or- (2/5)(sqrt5)
and k is approximately -0.11 or -1.89
so, z^2 = -0.11 or -1.89
z = +or- 0.33i   or  +or- 1.38i
where 'i' is the complex number sqrt(-1)

I hope you understand it.
Regards.