how-to-evaluate-ln-i-i-1-

Question Number 91936 by MWSuSon last updated on 03/May/20

h o w t o e v a l u a t e l n (i), i = \sqrt{- 1} .

Commented by MWSuSon last updated on 03/May/20

thank you sir, but what if I'm looking for log(i) in base 2 or 10?

Commented by mr W last updated on 03/May/20

\log_{10} (i) = \frac{\ln (i)}{\ln 10} = \frac{π}{2 \ln 10} i

\log_{2} (i) = \frac{\ln (i)}{\ln 2} = \frac{π}{2 \ln 2} i

\dots

Commented by MWSuSon last updated on 03/May/20

oh I see, change of base. Thank you sir.

Commented by mr W last updated on 03/May/20

i = e^{\frac{π i}{2}}

\ln (i) = \ln (e^{\frac{π i}{2}}) = \frac{π}{2} i

Commented by MWSuSon last updated on 03/May/20

s i r s o t h e s o l u t i o n o f t h i s e q u a t i o n

2^{(x + 1)} = i

w o u l d p r o c e e d a s f o l l o w s ?

x + 1 = {l o g}_{2} i

x = {l o g}_{2} i - 1

x = \frac{l n i}{l n 2} - 1

x = \frac{π}{2 l n 2} i - 1 ?

Commented by mr W last updated on 04/May/20

y e s

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