anonymous
  • anonymous
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))
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
pls :((((
anonymous
  • anonymous
The modulo of the complex number is correct
anonymous
  • anonymous
okay so instead of 5pi/6 it should be 2pi/3? I'm not sure why though

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More answers

anonymous
  • anonymous
Correct, its 2pi/3
anonymous
  • anonymous
I did arctan (2*sqrt(3) /2)
anonymous
  • anonymous
To find the angle of a complex number, you apply the following formula: \[\arg(z) = \frac{ \Im(z) }{ \Re(z) }\]
anonymous
  • anonymous
\[\arg(z) = \tan^{-1} \frac{ \Im(z) }{ \Re(z) }\]
anonymous
  • anonymous
I missed the arctan in the previous formula.
anonymous
  • anonymous
You missed the negative sign in your arctan.
anonymous
  • anonymous
arctan (2sqrt(3) / -2)?
anonymous
  • anonymous
Correct.
anonymous
  • anonymous
converted to radians it's (-pi/3) right? so where does the 2 come from?
anonymous
  • anonymous
You will get \[-\frac{ \pi }{ 3 }\]
anonymous
  • anonymous
Recall that you can add an angle by 2pi at any time, especially to make it positive.
anonymous
  • anonymous
-pi/3 + 2pi = 5pi/3 -pi/3 - 2pi = -7pi/3??? I feel like I'm missing something obvious..:/
anonymous
  • anonymous
Well, do recall that arctan, along with other inverse trig functions, is a multi-valued function.
anonymous
  • anonymous
-pi/3 is only one of the possible solutions.
anonymous
  • anonymous
Remember tangent is negative in both the second and fourth quadrants.
anonymous
  • anonymous
I don't know how to find a value in another quadrant if it's not on the unit circle
anonymous
  • anonymous
It's on the unit circle. You know that your first solution is -pi/3, which is 5pi/3 in the fourth quadrant.
anonymous
  • anonymous
Your second solution must be \[\pi - \frac{ \pi }{ 3 } = \frac{ 2 \pi }{ 3 }\]
anonymous
  • anonymous
why do you subtract it from pi?
anonymous
  • anonymous
It's the unit circle. You subtract from the quadrant. You subtract from pi for the second quadrant.
anonymous
  • anonymous
Oh wow. I never learned that... Thank you so much for your help!

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