Question

Find the value of the complex number $(i^{25}{)}^3$.

Answer 1

Simplifying ${\left(i^{25}\right)}^3$.

${\left(i^{25}\right)}^3=i^{75}$

$=i^{72+3}$

$=i^{72}\times i^3$

$=i^{4\times 18}\times i^3$

$={\left(1\right)}^{18}\times \left(-i\right)$

$=-i$