Question

Express the complex number in trigonometric form.

-4

Answer 1

You can rewrite -4 as -4+0i, right?

Answer 2

I don't really know to be honest.

Answer 3

I think that you can understand this.
-4=-4+0i

Answer 4

Have you learned complex plane, yet?

Answer 5

No but I have these answer choices I just don't know how to get to them.
4(cos 270° + i sin 270°)

4(cos 90° + i sin 90°)

4(cos 0° + i sin 0°)

4(cos 180° + i sin 180°)

Answer 6

I'll guide you of how to get to the correct answer.
First, both of us agree that -4=-4+0i
Secondly, have you learned complex plane, yet?
It looks something like the above drawing.

Answer 7

Yeah but what do we do with that?

Answer 8

Ok. Can you plot -4+0i on the complex plane?

Answer 9

@faariat

Answer 10

still there?

Answer 11

I'm aware of what the plane is but I don't know how to use it @science0229

Answer 12

right?

Answer 13

Now, the 'trigonometric form' of a+bi is\[\sqrt{a^2+b^2}(\cos \theta+i \sin \theta)\] where theta is the angle made by a+bi.

Answer 14

Here, a=-4, b=0, and theta=180 degrees.
Substitute those values in to get your answer.

Answer 15

I'm guessing that you're lost?

Answer 16

@faariat

Answer 17

I'm working it out right now

Answer 18

what do you do when you get 4(costheta+isintheta)?

Answer 19

what is theta in this problem?

Answer 20

Look at the second drawing.
I labeled the angle there.

Answer 21

180?

Answer 22

exactly!

Answer 23

oh so its just 4(cos180+isin180)

Answer 24

yep.

Answer 25

how do we do this if the number was -6i instead of -4?

Answer 26

Try it!
-6i=0-6i
So a=0, b=-6.
You can find theta by plotting it on the complex plane.

Answer 27

how do you plot -6i on the plane?

Answer 28

so 270?

Answer 29

Yep

Answer 30

this is the answer 6(cos 270° + i sin 270°)?

Answer 31

Yeah! You got it.

Answer 32

Any other questions?