The value of z is -1 + i√3.
To evaluate z^{60}, you can substitute -1 + i√3 for z in the expression. This will give you (-1 + i√3)^{60}, which can be simplified using the binomial theorem.
The binomial theorem states that for any real or complex numbers a and b, and any positive integer n, the expansion of (a + b)^n can be written as the sum of n+1 terms. This can be expressed as (a + b)^n = \sum_{k=0}^{n} \binom{n}{k} a^{n-k}b^k, where \binom{n}{k} is the binomial coefficient.
Using the binomial theorem, we can write (-1 + i√3)^{60} as \sum_{k=0}^{60} \binom{60}{k} (-1)^{60-k}(i√3)^k. This can be further simplified to \sum_{k=0}^{60} \binom{60}{k} (-1)^{60-k} (i^{2})^{k} 3^{k/2}. Since i^{2} = -1, the term (i^{2})^{k} will alternate between -1 and 1 as k increases. Thus, the final simplified form is \sum_{k=0}^{60} \binom{60}{k} (-1)^{k} 3^{k/2}.
The value of z^{60} for z = -1 + i√3 is approximately 3.0194 x 10^{31}.