Question

Complex Numbers in Trigonometric Form and DeMoivre's Theorem for Roots
Represent the complex number graphically, and find the trigonometric form of the number.

Answer 1

-2-2i

Answer 2

So far: -2-2i, r=sqrt(4+4)=sqrt(8)=2sqrt(2)
tan theta=-2/-2=1=7pi/4?

Answer 3

Or no because its not negative one..

Answer 4

you need
\[r=\sqrt{(-2)^2+(-2)^2}=\sqrt{8}=2\sqrt{2}\]

Answer 5

Which i've done :)

Answer 6

you also need
\[\theta =\frac{5\pi}{4}\] although of course it is not uniqu

Answer 7

Then i get tan theta= -2/-2=1. How did you get 5 pi/4?

Answer 8

5pi/4=225 degrees, which I understand, but I'm not sure where you actually got the 5pi/4 from from tan=1.

Answer 9

you just have to look and see where you are in the coordinate plane
in this case you have both x and y negative, so you are to the left and down. that is how you find the angle
you know
\[\tan(\theta)=1\] but you have to look to see what quadrant you are in to find
\[\theta\]

Answer 10

Is it tan theta=1 because -2sqrt(2)/-2sqrt(2)=1? Since tan=y/x?

Answer 11

this has nothing to do with converting from degrees to radians. it is the measure of the angle you are looking for,and it is not unique

Answer 12

I feel like I'm either going way too into it, or not enough. But I was just stating the 225 degrees because of your drawing.

Answer 13

\[a+bi=r\left(\cos(\theta)+i\sin(\theta)\right)\]
\[r=\sqrt{a^2+b^2}\]
\[\tan(\theta)=\frac{b}{a}\]

Answer 14

if you are working in radians (aka numbers) forget degrees.

Answer 15

So if tan theta=b/a, and b=4 and a=4, arctan(1)=theta?

Answer 16

that represents and angle of
\[\frac{5\pi}{4}\]

Answer 17

wait slow

Answer 18

I'm using a different chapter of knowledge for this because my online textbook is reffering to a chapter I was not in the class for.

Answer 19

\[\tan(\theta)=\frac{b}{a}\] but that does not mean
\[\arctan(\frac{b}{a})=\theta\]!!

Answer 20

Well it works out in this case...

Answer 21

no it does not

Answer 22

Here's the method to my madness, and we are getting the same answer:

Answer 23

arctan has range from
\[-\frac{\pi}{2}\] to
\[\frac{\pi}{2}\] so it will only work if you are in quadrant I or IV

Answer 24

tan(theta)=b/a
b=4
a=4
arctan(1)=theta
45 degrees=theta
ASTC,
45+180=225 degrees.

Answer 25

if you are in quadrant II or III you have to figure out what the angle is. you can use arctan, but if you are in the wrong quadrant you have to adjust

Answer 26

acually
\[a=-2, b=-2\] but you are right
\[\frac{b}{a}=1\] and you are also rigth that you need to add
\[\pi\] to
\[\frac{\pi}{4}\] to get the right angle