Argument value in complex numbers in polar form.

[kayanian]

-1-(under root)3 i
here we find that
r=2(hypotenuse)
a=-1(base)
b=-(under root)3

when i take sin theat= p/h=-(under root)3 / 2
theat from sin is -60

when i take cos theta = b/h =-1 / 2
which gives 120

now one is -60 and other is 120, which is the angel , i have to follow and what do i add it to?

 

[HallsofIvy]

Think about where $-1- \sqrt{3}i$ is on the complex plane. It has negative real part and negative imaginary part so it is in the third quadrant. Neither -60 or 120 degrees is in the third quadrant- they are both wrong.

tan(theta)= -sqrt{3}/-1= sqrt(3) gives theta= 60 degrees but since this number is in the third quadrant, theta= 180+ 60= 240 degrees.

cos(240)= -1/2 and sin(210)= -sqrt(3)/2.

 

[kayanian]

Think about where $-1- \sqrt{3}i$ is on the complex plane. It has negative real part and negative imaginary part so it is in the third quadrant. Neither -60 or 120 degrees is in the third quadrant- they are both wrong.

tan(theta)= -sqrt{3}/-1= sqrt(3) gives theta= 60 degrees but since this number is in the third quadrant, theta= 180+ 60= 240 degrees.

cos(240)= -1/2 and sin(210)= -sqrt(3)/2.

So the answer is :

2{cos 120+ i sin 120)
= 2 cis 120
??

but my solution manual gave me this answer

2 Cis 210
which i myself think is wrong

the table of cos and sin positive value is also used if i m right.and when cos and sin are yielding different results, we go to tangent.ok i get it now but i m lil confused because my solution manual gave wrong answer so please confirm.

 

[Elucidus]

2cis210 is incorrect. As HallsofIvy mentioned the correct argument is 240.

--Elucidus