evluate i^-50 where I is iota
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Verified answer
Correct question:
Evaluate i⁻⁵⁰ where i is a complex number or imaginary number
Solution:
As we know that
i is a complex number which is equal to √-1
Now , i⁻⁵⁰ can be written as
→ i⁻⁵⁰
We know that
a⁻ⁿ = 1/aⁿ
Similarly
→ 1/i⁵⁰
→ 1/(i⁴⁸ × i²)
Here , i is raised to any multiple of 4 is equal to 1 & i = √-1
→ 1/1 × (√-1)²
→ 1/1 × (-1)
→ 1/(-1)
→ - 1
Hence , i⁻⁵⁰ = - 1
•
As we know that :-
The value of i (iota) = √-1
Squaring on both sides
Now we have to find the value of
By the identity
As i² = -1
We know that -1^even integers = 1 and -1^odd integers = -1
As 25 is an odd number