Question

The value of $i^{57}+\frac{1}{i^{125}}$ is :

• A. $0$
• B. $-2i$
• C. $2i$
• D. $2$

Answer 1

The correct option is A $0$

$i^{57}+\frac{1}{i^{125}}$
$=i^{56}\cdot i+\frac{1}{i^{124}\cdot i}$
$=(i^4{)}^{14}.i+\frac{1}{(i^4{)}^{31}i}$
$=1\times i+\frac{1}{1\times i}$ $[\because i^4=1]$
$=i+\frac{i}{i^2}$
$=i-i$ $[\because i^2=-1]$
$=0$