Question

If z=-1-isquare root of 3,
Then arg (z)=?

Answer 1

Answer:

$- 2\pi \div 3$

Step-by-step explanation:

z=-1-iroot3 (z=x+iy)

arg(z)=taninverse(y/x) also we have to see the sign of x and y

therefore arg=taninverse(root3)

=pi/3

it should be in third quadrant as both x and y are negative

also arg must be in between (-pi to pi)

for all these conditions to happen the answer must be -2pi/3

it could be easily understood by plotting the complex number on the cartesian graph

i dont know how to insert the graph

but i can help

plot( -1,-root3) on the coordinate graph

join the point with the origin

the arg is always measured from positive x axis

so there are two options

one that u can go clockwise and the other is u can go anticlockwise

if u go anticlockwise u will get a value of arg greater than pi

so u will go clockwise and the measured angle between the line and positive x axis would be your answer and as u have gone clockwise it would be negative

reply if u understood