Question

Write the complex number in trigonometric form r(cos theta + i sin theta), with theta in the interval 0-360 degree
-7 +7i*(square root 3)

i got tan(theta)= - square root 3
so theta has to be 120 or 300 degree but why we use only 120?

Answer 1

@zepdrix

Answer 2

Because if you look back at your components...
The real component (x) is negative,
and the complex component (y) is positive,

which puts us in quadrant 2, yes?

Answer 3

Looks like you found the correct angles!
Just relate them back to your complex value to see which angle will actually work for you.

Answer 4

And I meant imaginary component (y)*
the whole thing is complex, I shouldn't have called it that hehe

Answer 5

hmmmm

Answer 6

confused? :o

Answer 7

im just wondering why dont we use the 300 angle lol

Answer 8

oh ok gotcha

Answer 9

x= r cos theta
y= r sin theta
so they need to be in QII

Answer 10

Yah, we're in quadrant 2 based on the components we were given.

The reason we came up with two angles is because information is lost when you use this:\[\Large\rm \arctan \frac{y}{x}=\theta\]See how the y and x are just kinda smashed together?
It doesn't tell us which one was negative, the y or x, when we combine them in this relationship.

So it gave us the two possible angles,
x negative, y positive produced 120,
x positive, y negative produced 300.