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

1685 208 Complex Numbers and Quadratic Equations Report Error

A

0

51%

B

2i

28%

C

-2i

15%

D

2

6%

Solution:

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