Question

PLEEEEEEEEEEEEEEEEEEEEEEEEEEEASE
Check my answer for a medal?

Express the complex number in trigonometric form.

-2 + 2(square root of three)i

I got 4(cos(5pi/6) + i sin(5pi/6))

Answer 1

pls :((((

Answer 2

The modulo of the complex number is correct

Answer 3

okay so instead of 5pi/6 it should be 2pi/3? I'm not sure why though

Answer 4

Correct, its 2pi/3

Answer 5

I did arctan (2*sqrt(3) /2)

Answer 6

To find the angle of a complex number, you apply the following formula: \[\arg(z) = \frac{ \Im(z) }{ \Re(z) }\]

Answer 7

\[\arg(z) = \tan^{-1} \frac{ \Im(z) }{ \Re(z) }\]

Answer 8

I missed the arctan in the previous formula.

Answer 9

You missed the negative sign in your arctan.

Answer 10

arctan (2sqrt(3) / -2)?

Answer 11

Correct.

Answer 12

converted to radians it's (-pi/3) right? so where does the 2 come from?

Answer 13

You will get \[-\frac{ \pi }{ 3 }\]

Answer 14

Recall that you can add an angle by 2pi at any time, especially to make it positive.

Answer 15

-pi/3 + 2pi = 5pi/3
-pi/3 - 2pi = -7pi/3???
I feel like I'm missing something obvious..:/

Answer 16

Well, do recall that arctan, along with other inverse trig functions, is a multi-valued function.

Answer 17

-pi/3 is only one of the possible solutions.

Answer 18

Remember tangent is negative in both the second and fourth quadrants.

Answer 19

I don't know how to find a value in another quadrant if it's not on the unit circle

Answer 20

It's on the unit circle. You know that your first solution is -pi/3, which is 5pi/3 in the fourth quadrant.

Answer 21

Your second solution must be \[\pi - \frac{ \pi }{ 3 } = \frac{ 2 \pi }{ 3 }\]

Answer 22

why do you subtract it from pi?

Answer 23

It's the unit circle. You subtract from the quadrant. You subtract from pi for the second quadrant.

Answer 24

Oh wow. I never learned that... Thank you so much for your help!