How many roots have a complex number with irrational exponent?
Solution 1:
Let's take a simple example: $\sqrt[\Large\pi]1=\Big(e^{2k\pi~i}\Big)^\frac1{\Large\pi}=e^{2ki}=\cos\big(2k\big)+i\sin\big(2k\big)$, for all $k\in\mathbb Z$.
How many roots have a complex number with irrational exponent?
Solution 1:
Let's take a simple example: $\sqrt[\Large\pi]1=\Big(e^{2k\pi~i}\Big)^\frac1{\Large\pi}=e^{2ki}=\cos\big(2k\big)+i\sin\big(2k\big)$, for all $k\in\mathbb Z$.