Question

Evaluate ( i^37 + 1/i^67)​

Answer 1

$i^{37}+\dfrac{1}{i^{67}}=\\\\(i^4)^9\cdot i+\dfrac{1}{(i^4)^{16}\cdot i^3}=\\\\1^9\cdot i+\dfrac{1}{1^{16}\cdot (-i)}=\\\\i+\dfrac{1}{-i}=\\\\i+\dfrac{i}{1}=\\\\2i$