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    Euler's Identity and i: how to solve e^(pi*i) = -1 for i

    I was trying to solve for x. I was trying to solve for i. i should be the square root of -1 however there should be no real answer to the square root of -1 so the square root of -1 is a different type of number which we call i. What I was trying to figure out is if there was way, through Euler's...
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    Euler's Identity and i: how to solve e^(pi*i) = -1 for i

    I tried taking logs of both sides and using the property rule. I got stuck at pi*i log e = 2log i and from log e^(pi*i)=log i^2.
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    Euler's Identity and i: how to solve e^(pi*i) = -1 for i

    I'm not sure how to do logs with complex exponents which is why I asked if anyone knew how and what the answer would be.
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    Euler's Identity and i: how to solve e^(pi*i) = -1 for i

    There was something interesting that I found out when looking at Euler's Identity. If e^(pi*i) = -1 and i^2 = -1 then e^(pi*i) has to equal i^2 to get the equation seen here. e^{\pi \cdot i} = i^{2} My question is can you in this equation solve for i and if you can what would you get? Will i...
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