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/sci/ - Science & Math

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5778322 No.5778322 [Reply] [Original]

Not a shitpost here, but.
They say i^i=e^(-pi/2) or whatever (didn't google) but I hear i^i has multiple values, what are other values for i^i?

>> No.5778328

you heard wrong

>> No.5778347

exp(15003 pi/2)

>> No.5778377

>>5778322
i^i=e^(i*ln i)=e^(i*(i*pi/2))=e^(-pi/2)

>> No.5778384

Yes, the complex logarithm is multivalued.

>> No.5778387

>>5778347
7/10 almost right, try harder next time

>> No.5778389

>>5778328
No, it has infinitely many values.
<span class="math"> i^{i} = e^{\pi (2n - 1/ 2 ) } [/spoiler]
Look up the complex logarithm, OP.

>> No.5778646

>>5778389
Then why do people say "omg i^i=e^(-pi/2) so emazin".

>> No.5778677

>>5778646
because a complex number to a complex power is real in this case.

>> No.5778688

>>5778646
Because imaginary to the power of imaginary is real.