Originally Posted by

**Plato** **I totally disagree with that quote.**

Any problem dealing with complex exponentiation is definitely a university level: perhaps number theory or analysis.

Complex exponents do not behave as expected.

For example, if each of $\displaystyle u,~v,~\&~w$ is a complex number then $\displaystyle [u^v]^w\not=u^{vw}$.

Only in the case that $\displaystyle n\in \mathbb{Z}$ can we say that $\displaystyle [u^v]^n\not=u^{nv}$

Thus as applied to this problem it can be said that $\displaystyle t^{4i}=[t^i]^4$.

Here is a further compilation: $\displaystyle t^i=\exp[i\log(t)]$ where $\displaystyle \log(t)=\ln(|t|)+i\;\text{arg}(t)$.

It is not clear if t is a complex variable or a real variable.