1.

Find the modulus and argument of each of the following complex number: `-sqrt(3)-i`

Answer» Correct Answer - `2,(-5pi)/(6),2{cos((-5pi)/(6))+i sin((-5pi)/(6))}`
Let `z = -sqrt(3) - i rArr r^(2) = |z|^(2) = (-sqrt(3))^(2)+(-1)^(2)=4 rArr r = |z| = 2`.
`tan alpha=|(-1)/(-sqrt(3))|=(1)/(sqrt(3))rArr alpha = (pi)/(6)`.
The given number represents the point `P(-sqrt(3), -1)` which lies in the third quadrant.
`therefore" "arg(z)=theta=-(pi-alpha)=-(pi-(pi)/(6))=(-5pi)/(6)`.
`therefore" "z=2[cos((-5pi)/(6))+i sin((-5pi)/(6))]`.


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