Is 3^2i equal to the 2i root of 0.0123456789...
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Is 3^2i equal to the 2i root of 0.0123456789...

[From: ] [author: ] [Date: 11-12-20] [Hit: ]
-I highly doubt it.-0.58625493429... + i 0.......
I was solving something using two different methods and I was supposed to get the same answers but in different forms. Are these the same answers but just in different forms?

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That is a weird question.

By the "2i root of 0.0123456789" I suppose you mean (1/81) raised to the power of (1/2i):

(1/81)^(1/2i)=(3^(-4))^(1/2i)=3^(-4/2i… so you are correct!

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I highly doubt it.

3^(2i) =
[e^ln(3)]^(2i) =
e^(2i ln(3)) =
cis(2 ln(3)) =
cos(2 ln(3)) + i sin(2 ln(3)) ≈
-0.58625493429... + i 0.81012662715099
a complex value

As for taking the (2i) root. It is the same as raising a number to the power of (1/(2i)), which is simplified to (-i/2)

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No
1
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