` z= -1-isqrt(3)` find argument and modulus of given complex number

Options

A. `-240^(@)`
B. `-120^(@)`
C. `120^(@)`
D. `60^(@)`

Answer

B

Explanation

Let ` -1-isqrt(3)=r(costheta+isintheta)`
`rArr" "rcostheta=-1`
and `" "rsintheta=-sqrt(3)`
`" "thereforer^(2)cos^(2)theta+r^(2)sin^(2)theta=1+_3 rArr" "r^(2)=4 `
`rArr" "r=2`
and `" "(rsintheta)/(rcostheta)=(- sqrt(3))/(-1)`
`" "rArr" "tantheta =sqrt(3)=tan60^(@)`
`" "=tan(180^(@)+60^(@))`
`" "because sin and cos ` are negative in third quadrant.
`rArr" "theta=240^(@)`
`therefore` modulus = 2, argument = `240^(@)`