Question

find modulus and argument of √3-i​

Answer 1

Answer:

modulus =2

argument= 5pi/6

Step-by-step explanation:

modulus of complex no. (a+ib)=(a²+b²)½ => 3½−i = [(3½)²+(1)²]½

=> 3½-i =[3+1]½=4½=2

for argument

let z= 3½-i

3½-i=r(cosø +isinø)

squaring and adding both sides

we get

r²=(3½)²+(-1)²

r=2

equating the coefficient we get

rcosø=3½ & rsinø=1

cosø=3½/2 & sinø=-1/2

tanø=(-1/3½)

|tanø|=| 1/3½ |

ø=pi/6

now ø lies in 2nd quadrant

therefore ,

ø=(pi - pi/6)=5pi/6

which is required ans.

hope you understand mate