Evaluate the following:
i)
ii)
iii)
Answers
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3
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 !
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