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Popular >

simplify ln(5e^{-i(7pi)/4})

Solution

simplify

ln (5 e^{- i \frac{7 π}{4}})

Solution

ln (5) - \frac{7 πi}{4}

Solution steps

ln (5 e^{- i \frac{7 π}{4}})

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

ln (5 e^{- i \frac{7 π}{4}}) = ln (5) + ln (e^{- i \frac{7 π}{4}})

= ln (5) + ln (e^{- i \frac{7 π}{4}})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (e^{- i \frac{7 π}{4}}) = - i \frac{7 π}{4} ln (e)

= ln (5) - i \frac{7 π}{4} ln (e)

i \frac{7 π}{4} ln (e) = \frac{7 πi}{4}

= ln (5) - \frac{7 πi}{4}

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Frequently Asked Questions (FAQ)

What is ln(5e^{-i(7pi)/4}) ?
The solution to ln(5e^{-i(7pi)/4}) is ln(5)-(7pii)/4