Question

Express the complex number in trigonometric form.
-3 + 3 √3i

Answer 1

One trick for you

Answer 2

\[r=\sqrt{a^2+b^2}\]

Answer 3

\[\theta=\tan^{-1}\left(\frac ba\right)\]

Answer 4

Hmm how do I apply this?

Answer 5

Talking about a+bi ahaha

Answer 6

Never mind, you may have another method

Answer 7

I got -60 for the tan-1 lol not sure what to do

Answer 8

You may wish to call it arctangent instead of tan-1, and the -60 should be in degrees

Answer 9

Make it positive

Answer 10

Ah I'm confused now, sorry

Answer 11

Okay find r first and sorry for confusing you

Answer 12

okay so r = √a^2+b^2
so √-3+3√3i right?

Answer 13

Well (1) you forgot to square and (2) the b doesn't include the i

Answer 14

Ahh okay thanks! Let me try it now

Answer 15

3.5

Answer 16

?

Answer 17

I put it in my calculator and that's what I got lol

Answer 18

Put in your calculator \(\sqrt{3^2+(3\sqrt3)^2}\)

Answer 19

Now its 4.2

Answer 20

Actually

Answer 21

Don't use your calculator

Answer 22

Okay

Answer 23

So now what do I do?

Answer 24

Well calculate \(\sqrt{3^2+(3\sqrt3)^2}\)

Answer 25

With my calculator? lol

Answer 26

lol without

Answer 27

√12

Answer 28

Well it's \((3\sqrt3)^2\) not \((\sqrt3)^2\) inside

Answer 29

Okay my calculator said something else but would it be 6? Because it would be √36?

Answer 30

\[\sqrt{3^2+(3\sqrt3)^2}=\sqrt{9+27}=\sqrt{36}=6\]

Answer 31

So back to the question

Answer 32

Express it in trigonometric form

Answer 33

Yep

Answer 34

What's the trigonometric form?

Answer 35

z=r(cosα+i⋅sinα)

Answer 36

so the r is 6

Answer 37

Yes

Answer 38

6(cosx+isinx)

Answer 39

Now we need to find the cos x and sin x right

Answer 40

And I have to apologize for my accent that seems rude because I'm not in my full mood currently

Answer 41

The x is -60deg

Answer 42

It's alright!! and okay how do I convert that to degrees again

Answer 43

-60deg is already degrees

Answer 44

The problem is how to make that positive

Answer 45

Oh haha okay how do I do that

Answer 46

What's a full circle?

Answer 47

360

Answer 48

Add it to that

Answer 49

360+-60 = 300

Answer 50

Exactly

Answer 51

Back to the ques

Answer 52

Trig form, okay hmm
cos(300)?

Answer 53

Well

Answer 54

6(cos300+isin300)

Answer 55

Ahh gotcha so now I have to relate it to the unit circle or something

Answer 56

Yep

Answer 57

The trigonometric enables you to plot the point on the Argand's diagram or however it's called coz I can't forking spell

Answer 58

Okay so the point on the unit circle is 5pi/3 or (1/2, -√3/2)