assuming $Z$ is a complex number i.e $a + bi$. we have
$Z^2 = (a + bi)^2 = (a^2-b^2)+(2ab)i$
$Z^3 = (a+bi)^3 = (a^3-3ab^2) - (b^3-3a^2b)i$
but what would be the general formula for computing $Z^n$ where n is any real number?
I wanted to use this method but i dont know how the computation goes for complex number $i$. also I want to do this computation on a computer so i have to keep real and imaginary parts separated from each other.
I know that i can only approximate numbers when $n$ is not an integer. but thats ok.
Is this even possible?