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!
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)
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