Question

Evaluate the following:
i) $i^{116}$
ii) $i^{403}$
iii) $\frac{1}{i^{58}}$

Answer 1

Answer:

i) 1

ii) -i

iii) -1

Step-by-step explanation:

Hi,

We know that i² = -1  

i⁴ = (i²)² = (-1)² = 1

i) i¹¹⁶ = (i⁴)²⁹ = (1)²⁹ = 1

ii) i⁴⁰³ = i⁴⁰⁰⁺³ = i⁴⁰⁰*i³ = (i⁴)¹⁰⁰*i³ = (1)¹⁰⁰*i²*i

= -i

iii) 1/i⁵⁸

Multiplying and dividing by i², we get

1/i⁵⁸ = i²/(i⁸*i²) = i²/i⁶⁰ = i²/(i⁴)¹⁵ = i²/1 = i²

= -1

Hope, it helps !