If `z=cos(pi/4)+isin(pi/6)` , then
a. `|z|=1, arg(z)=\ pi/4`
b. `|z|=1, arg(z)=\ pi/6`
c. `|z|=(sqrt(3))/2, arg(z)=(5pi)/(24)`
d. `|z|=(sqrt(3))/2, arg(z)=tan^(-1)(1/sqrt(2))`

Explanation

`|z|=(sqrt(3))/2, arg(z)=tan^(-1)(1/sqrt(2))`
`z=cos frac{pi}{4}+i sin frac{pi}{6} `

`Rightarrow z=frac{1}{sqrt{2}}+frac{1}{2} i `

`Rightarrow|z|=sqrt{(frac{1}{sqrt{2}})^{2}+frac{1}{4}} `

`Rightarrow|z|=sqrt{frac{1}{2}+frac{1}{4}} `

`Rightarrow|z|=sqrt{frac{3}{4}}`

`Rightarrow|z|=frac{sqrt{3}}{2} `

`tan alpha=|(Im{z})/(Re{z}) | `

`=frac{1}{sqrt{2}} `

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