What is ln(1/(sqrt(-1)+1)) ?

The solution to ln(1/(sqrt(-1)+1)) is -ln(1+i)

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simplify ln(1/(sqrt(-1)+1))

simplify

ln (\frac{1}{- 1 + 1})

- ln (1 + i)

Solution steps

ln (\frac{1}{- 1 + 1})

Apply log rule:

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

ln (\frac{1}{- 1 + 1}) = ln (1) - ln (- 1 + 1)

= ln (1) - ln (1 + - 1)

Apply log rule:

lo g_{a} (1) = 0

= 0 - ln (1 + - 1)

Apply imaginary number rule:

- 1 = i

= 0 - ln (1 + i)

0 - ln (i + 1) = - ln (i + 1)

= - ln (1 + i)

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