Question

Express the complex number in trigonometric form.
-2

Answer 1

Here is a good way to get started,\[\large\rm -2\quad=\quad -2+0i\]So what does this tell us?
We have no imaginary component,
no vertical component.

So our value lies on `the real axis`, yes?

Answer 2

Would the answer be 2(cos 0° + i sin 0°)? I have 2 for R and the angle as arctan(0).

Answer 3

Well there's a nice easy way to check your work.
Simplify cos0 and sin0.

cos 0 = 1
sin 0 = 0
right?

So you end up with 2(1+0i)

Hmm that doesn't give us the -2 we need :(

Answer 4

you had arctan(0)?
Ok that's good.

arctangent will always spit out this principle value in the first or fourth quadrant though.

Notice that -2 is along the negative real axis.
So it's between quadrants 2 and 3.
We can take our angle that we ended up with and add 180 to it.
(Because tangent is periodic in 180 degrees).

Answer 5

so 2(cos 180° + i sin 180°)?

Answer 6

Again, check your work.
What do you end up with?

Answer 7

cos180 = ?
sin180 = ?

Answer 8

2(-1 + 0i) right?

Answer 9

Ahh it worked out! Nice! :)
Yes good job.