Natural Number makes a difference

Algebra Level pending

Since we know that i = e i π / 2 i=e^{i\pi/2} , which of the following is correct one?

1. i i = e ( i ) ( i ) π / 2 = e π / 2 \large 1. i^i=e^{(i)(i)\pi/2}=e^{-\pi/2}

2. i i = i ( 1 ) 1 / 2 = ( i ) 1 / 2 = 2 2 ( 1 + i ) \large 2. i^i =i^{(-1)^{1/2}}=(-i)^{1/2}= \frac{\sqrt{2}}{2} ( -1 + i )

2 Both are wrong 1 Both are correct

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1 solution

Well, for the first one, barely applying Sir Euler's Formula can help us to obtain the answer, while for the second, it is just some kind of illusion that most maths lovers encounter in their lives. F o r E x a m p l e **For Example** ( 3 3 ) 2 = 3 6 = 729 (3^3)^2 = 3^6 = 729 , But ( 3 3 2 ) = 3 9 (3^{3^2} ) = 3^9

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