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))).`
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