dumbsearch2
  • dumbsearch2
TRIGONOMETRY: Write z = the square root of 3 minus i. in abbreviated trigonometric form.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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dumbsearch2
  • dumbsearch2
anonymous
  • anonymous
fist find the magnitude?
anonymous
  • anonymous
\[Z=x+i y\] \[|Z|=\sqrt{x^2+y^2}\]

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dumbsearch2
  • dumbsearch2
So I just plug in y as -1 and x as root(3)? That's all there is to it?
anonymous
  • anonymous
yes @dumbsearch2
dumbsearch2
  • dumbsearch2
Then what?
anonymous
  • anonymous
\[\Theta=\tan^{-1}(\frac{ y }{ x }) =\]\[\Theta=\tan^{-1}(\frac{ -1 }{ \sqrt{3} })=-30^0\] in fourth quarter
dumbsearch2
  • dumbsearch2
What is that?
anonymous
  • anonymous
|dw:1441111202672:dw|
dumbsearch2
  • dumbsearch2
I did: |Z| = root((root(3))^2+(-1)^2) and I found: |Z| = 2. What now?
anonymous
  • anonymous
complex number: magnitude + angle
dumbsearch2
  • dumbsearch2
How should I proceed? I found that |Z| = 2.
anonymous
  • anonymous
this the magnitude, and now we should find the angle
anonymous
  • anonymous
\[\Theta=\tan^{-1}(\frac{ y }{ x }) =\]\[\tan^{-1}(\frac{ -1 }{ \sqrt{3} })=-30^0\]
anonymous
  • anonymous
\[Z=x+iy=re^{i \theta}=r(\cos \theta+isin \theta)\]=\[rCis\] and\[r=|Z|\]
anonymous
  • anonymous
r=|Z|=2
anonymous
  • anonymous
\[\theta=-30^0=330^0\]
anonymous
  • anonymous
Plug values of r & θ in: (rCis θ)
dumbsearch2
  • dumbsearch2
Thank you so much! Most importantly, I know how to do the problem by myself now, in the clear manner in which you explained it... thanks a million!
anonymous
  • anonymous
@dumbsearch2 no problem, you are welcome in any time.
dumbsearch2
  • dumbsearch2
I want to do the same thing for the next problem: "Write z = -5 in abbreviated trigonometric form." However, why isn't there an i? Also how can I find the x and the y for the magnitude if there is only one variable (-5)?
anonymous
  • anonymous
I finished complex course since 1 year only. it is interesting.
anonymous
  • anonymous
Z=-5+i0
anonymous
  • anonymous
x=-5, y=0
dumbsearch2
  • dumbsearch2
Thank you!
dumbsearch2
  • dumbsearch2
|Z| = 5, right?
anonymous
  • anonymous
|dw:1441112765839:dw| not 0
dumbsearch2
  • dumbsearch2
5 cis 180 degrees is the solution
dumbsearch2
  • dumbsearch2
because a straight line is 180 degrees
dumbsearch2
  • dumbsearch2
right?
anonymous
  • anonymous
not, the angle is counted from positive x-axis
dumbsearch2
  • dumbsearch2
A. 5 cis 180 degrees B. -5 cis 0 degrees C. root(5) cis 180 degrees D. 25 cis 0 degrees
dumbsearch2
  • dumbsearch2
Which one?
anonymous
  • anonymous
A
dumbsearch2
  • dumbsearch2
thank you, I understand now.
anonymous
  • anonymous
Good luck

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