What is ln(4e^{-i pi/2})-ln(4e^{-pi/2 i}) ?

The solution to ln(4e^{-i pi/2})-ln(4e^{-pi/2 i}) is 0

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simplify ln(4e^{-i pi/2})-ln(4e^{-pi/2 i})

simplify

ln (4 e^{- i \frac{π}{2}}) - ln (4 e^{- \frac{π}{2} i})

0

Solution steps

ln (4 e^{- i \frac{π}{2}}) - ln (4 e^{- \frac{π}{2} i})

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

ln (4 e^{- i \frac{π}{2}}) - ln (4 e^{- i \frac{π}{2}}) = ln (\frac{4 e ^{- i \frac{π}{2}}}{4 e ^{- i \frac{π}{2}}})

= ln (\frac{4 e ^{- i \frac{π}{2}}}{4 e ^{- \frac{π}{2} i}})

\frac{4 e ^{- i \frac{π}{2}}}{4 e ^{- \frac{π}{2} i}} = 1

= ln (1)

Apply log rule:

lo g_{a} (1) = 0

= 0

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What is ln(4e^{-i pi/2})-ln(4e^{-pi/2 i}) ?
The solution to ln(4e^{-i pi/2})-ln(4e^{-pi/2 i}) is 0