3 items are filed under this topic.
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0^(a+bi) |
2020-12-03 |
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From Douglas:
I realize raising 0^a = 0 if a>0 and undefined if a<=0.
If have read that 0^bi is undefined for all b.
What I don't understand is why 0^(a+bi) = 0 if a and b are not equal to zero.
Is this purely by definition or is there a logical reason why this is the case?
(I have taken Complex Analysis, so have a fairly good understanding of complex numbers.)
Answered by Penny Nom. |
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I started with Euler's identity and manipulated it |
2011-11-14 |
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From anonymous:
I started with Euler's identity and manipulated it
e^i*pi=-1
e^-i*pi=(-1)^-1
e^-i*pi=-1
e^-i*i*pi=(-1)^i
e^--pi=(-1)^i
e^pi=(-1)^i
type it in in a calculator and you get e^pi=23.1406926... and
(-1)^i=0.0432139183... What did I do wrong?
Answered by Robert Dawson. |
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How do you raise a number to an imaginary/complex power? |
1996-07-03 |
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From Andy Golden:
How do you raise a number to an imaginary/complex power? I know how you raise "e" to a complex power, like e^(pi*i): cos pi + i * sin pi But what about numbers other than "e"? What if I want to raise 5 to the 2i power? How is that done?
Answered by Chris Fisher. |
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