Find the modulus and the arguments of the complex number `z=-sqrt()+i`

Answer

N/a

Explanation

Let `-sqrt(3)+i=r(costheta+isintheta)`
` rArr" "rcostheta=-sqrt(3)`
and `" "rsintheta=1`
`" "thereforer^(2)cos^(2)theta+r^(2)sin ^(2)theta=3+1`
`" "rArr" "r^(2)=4 " "rArr" "r=2`
and ` " "(rsintheta)/( rcostheta)=(1)/(-sqrt(3))`
`" "tantheta=-(1)/(sqrt(3))=-tan30^(@)`
`" "tan and cos ` are negative in second quadrant.
`rArr" "tan theta=tan(180^(@)-30^(@))`
`" "theta=150^(@)`
`therefore` Modulus =2, Argument = `150^(@)`