Question

Express the complex number in trigonometric form -6+6√3i

Answer 1

\[-6+\sqrt{3}i\]

Answer 2

What are x, and y in the expression?
Recall: x + iy is a form of an imaginary number.

Answer 3

\[-6+6\sqrt{3}i\]
sorry, i mistyped it

Answer 4

Arent they just coordinates?

Answer 5

doesn't matter, the same question, what are x, y?

Answer 6

(-6, 6√3)?

Answer 7

not that, take steps, please.
you have x = -6, y = 6sqrt 3
now find r, \(r^2 = x^2 +y^2\) show me r = ??

Answer 8

r=12?

Answer 9

yup, now, find \(\theta\)
\(tan\theta = \dfrac{y}{x}=??\)

Answer 10

-30

Answer 11

I got -60

Answer 12

i re-did it to make sure

Answer 13

ok, take your time, tag me after you get the answer

Answer 14

Oh im sorry i had switched x and y

Answer 15

-60 = 2pi/3
I think i remember the equation now

Answer 16

nope, you have to have a logic to switch -60 to 2pi/3

Answer 17

because

Answer 18

omg why do i keep making these little mistakes

Answer 19

Actually, the answer is 2pi/3, but you must put some argue on that to make the solution is perfect correct.

Answer 20

\[12(\cos \frac{ 5\pi }{ 3 }+isin \frac{ 5\pi }{ 3})\]

Answer 21

wait what...

Answer 22

That is the wrong one!!

Answer 23

So 2pi/3 is right? I'm a little confused

Answer 24

No confuse, =\(tan \dfrac{5\pi}{3}=tan\dfrac{2\pi}{3}= -\sqrt3\)
We pick 2pi/3 because the given x = \(\color{red}{-~}6\) so that the terminal point must be in quadrant 2.

Answer 25

That give us the final answer is \(12(cos\dfrac{2\pi}{3}+isin\dfrac{2\pi}{3}\))
got what I mean??

Answer 26

Tan=5pi/3=tan2pi/3? so why choose one over the other?

Answer 27

because x = -6 , y = +6sqrt3
x <0, y>0 , the point is in quadrant 2

Answer 28

OHHHHH