`6(cos((5pi)/12) + i sin((5 pi)/12))` Write the standard form of the complex number.

You need to go from trigonometric form in standard form of the complex number, hence, you just need to simplify it replacing the values of trigonometric functions for `cos (5pi/12)` and  `sin (5pi/12)` , such that:

`z = 6(cos (5pi/12) + i*sin (5pi/12))`

`cos(5pi/12) = cos (6pi/12 - pi/12) = cos(pi/2 - pi/12) = sin(pi/12)`

`sin(pi/12) = sin((pi/6)/2) = sqrt((1 - cos(pi/6))/2)`

`sin(pi/12) = (sqrt(2 - sqrt3))/2`

`sin(5pi/12) = cos(pi/12) = (sqrt(2 + sqrt3))/2`

`z = 6((sqrt(2 - sqrt3))/2 + i*(sqrt(2 + sqrt3))/2) `

`z = 3(sqrt(2 - sqrt3) + i*(sqrt(2 + sqrt3)))`

Hence, the standard form of the given complex number is `z = 3(sqrt(2 - sqrt3) + i*(sqrt(2 + sqrt3))).`