What is ln(2)+ln(1+sqrt(3)i) ?

The solution to ln(2)+ln(1+sqrt(3)i) is ln(2+2sqrt(3)i)

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simplify ln(2)+ln(1+sqrt(3)i)

simplify

ln (2) + ln (1 + 3 i)

ln (2 + 23 i)

Solution steps

ln (2) + ln (1 + 3 i)

Apply log rule:

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

ln (2) + ln (1 + 3 i) = ln (2 (1 + 3 i))

= ln (2 (1 + 3 i))

Rewrite

2 (1 + 3 i)

in standard complex form:

2 + 23 i

= ln (2 + 23 i)

ln (\frac{x ^{2}}{1 + x})

9 ln (x) - 3 ln (2 x^{3})

\frac{ln ( 2 )}{ln ( 3 ) + ln ( 2 )}

lo g_{10} (\frac{- 5}{x + 8})

ln (x) - \frac{1}{4} ln (v^{2} + 2)

What is ln(2)+ln(1+sqrt(3)i) ?
The solution to ln(2)+ln(1+sqrt(3)i) is ln(2+2sqrt(3)i)