MHB Complex numbers simplification

[Guest2]

If $z = e^{(2-\frac{i \pi}{4})}$ what's $z^5$?

The only way I can think of doing this is expanding $(2-\frac{i \pi}{4})^5$, but I think I'm supposed to use a simpler method (not sure what it's).

 

[I like Serena]

If $z = e^{(2-\frac{i \pi}{4})}$ what's $z^5$?

The only way I can think of doing this is expanding $(2-\frac{i \pi}{4})^5$, but I think I'm supposed to use a simpler method (not sure what it's).

Hi Guest, (Smile)

Let's substitute and apply a power rule:
$$z^5=\left(e^{(2-\frac{i \pi}{4})}\right)^5
=e^{5(2-\frac{i \pi}{4})}
$$

 

[Guest2]

Hi Guest, (Smile)

Let's substitute and apply a power rule:
$$z^5=\left(e^{(2-\frac{i \pi}{4})}\right)^5
=e^{5(2-\frac{i \pi}{4})}
$$

Thank you, I like Serena. I get it now. (Smile)