Mild Polarizer

Algebra Level 3

What is one of the values of

$\ln{ (1+i\sqrt { 3 } ) } = \ ?$

Details and Assumptions

$i^2 = -1$

i\ln{ 2 + } \frac { \pi }{ 3 }

None Of these choices

i\frac { \pi }{ 3 }

i\ln{ 2 + } i\frac { \pi }{ 3 }

\ln{ 2 + } i\frac { \pi }{ 3 }

1 solution

Saurav Pal
Apr 2, 2015

$x\quad =\log _{ e }{ (1+i\sqrt { 3 } ) } =\log _{ e }{ 2(\frac { 1 }{ 2 } } +i\frac { \sqrt { 3 } }{ 2 } )=\log _{ e }{ 2\quad +\quad } \log _{ e }{ (\frac { 1 }{ 2 } } +i\frac { \sqrt { 3 } }{ 2 } )\\ \Rightarrow \quad x\quad =\quad \log _{ e }{ 2\quad +\quad \log _{ e }{ (cos\cfrac { \pi }{ 3 } +i\quad sin\cfrac { \pi }{ 3 } )\quad =\quad } } \log _{ e }{ 2\quad +\quad \log _{ e }{ { e }^{ i\cfrac { \pi }{ 3 } } } } \\ \Rightarrow \quad x\quad =\quad \log _{ e }{ 2\quad +\quad i\frac { \pi }{ 3 } } .$

Mild Polarizer

1 solution

0 pending reports