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anonymous
 one year ago
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))
anonymous
 one year ago
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))

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0The modulo of the complex number is correct

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay so instead of 5pi/6 it should be 2pi/3? I'm not sure why though

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I did arctan (2*sqrt(3) /2)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0To find the angle of a complex number, you apply the following formula: \[\arg(z) = \frac{ \Im(z) }{ \Re(z) }\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[\arg(z) = \tan^{1} \frac{ \Im(z) }{ \Re(z) }\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I missed the arctan in the previous formula.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0You missed the negative sign in your arctan.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0arctan (2sqrt(3) / 2)?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0converted to radians it's (pi/3) right? so where does the 2 come from?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0You will get \[\frac{ \pi }{ 3 }\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Recall that you can add an angle by 2pi at any time, especially to make it positive.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0pi/3 + 2pi = 5pi/3 pi/3  2pi = 7pi/3??? I feel like I'm missing something obvious..:/

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Well, do recall that arctan, along with other inverse trig functions, is a multivalued function.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0pi/3 is only one of the possible solutions.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Remember tangent is negative in both the second and fourth quadrants.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I don't know how to find a value in another quadrant if it's not on the unit circle

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0It's on the unit circle. You know that your first solution is pi/3, which is 5pi/3 in the fourth quadrant.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Your second solution must be \[\pi  \frac{ \pi }{ 3 } = \frac{ 2 \pi }{ 3 }\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0why do you subtract it from pi?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0It's the unit circle. You subtract from the quadrant. You subtract from pi for the second quadrant.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh wow. I never learned that... Thank you so much for your help!
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