1. Tardigrade
  2. Question
  3. Mathematics
  4. i57+(1/i25), when simplified has the value

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. $i^{57}+\frac{1}{i^{25}}$, when simplified has the value

Complex Numbers and Quadratic Equations

Solution:

$i^{57}+\frac{1}{i^{25}}=\left(i^{4}\right)^{14} \cdot i+\frac{1}{\left(i^{4}\right)^{6} i}$
$=i+\frac{1}{i}=i-i=0$