Question

Can someone answer the question?​

Answer 1

`(√(3) )/(3) }(cos((19\pi)/(12))+isin((19\pi)/(12)))`

Explanation:

Division of complex numbers in polar form is
`z_1/z_2=(r_1)/(r_2)cis(\theta_1-\theta_2)` where
`z_1` and
`z_2` are the complex numbers being divided,
`r_1` and
`r_2` are the moduli,
`\theta_1` and
`\theta_2` are the arguments, and
`cis` is shorthand for
`cos\theta+isin\theta`. Therefore:

`(9(cos((11\pi)/(6))+isin((11\pi)/(6))) )/(3√(3)((cos(\pi)/(4))+isin((\pi)/(4))) )`

`(9)/(3√(3) )cis((11\pi)/(6)-(\pi)/(4))`

`(√(3) )/(3) }cis((19\pi)/(12))`

`(√(3) )/(3) }(cos((19\pi)/(12))+isin((19\pi)/(12)))`