dumbsearch2
  • dumbsearch2
Write z = -5 + 5i in trigonometric form.
Mathematics
schrodinger
  • schrodinger
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dumbsearch2
  • dumbsearch2
dumbsearch2
  • dumbsearch2
D?
anonymous
  • anonymous
|dw:1441163170659:dw|

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surry99
  • surry99
Hint:Sketch the point it on the complex plane
dumbsearch2
  • dumbsearch2
I found -(pi)/(4)
dumbsearch2
  • dumbsearch2
before
anonymous
  • anonymous
??
anonymous
  • anonymous
|dw:1441163275849:dw|
dumbsearch2
  • dumbsearch2
What does that graph mean?
jim_thompson5910
  • jim_thompson5910
-5 + 5i is in the form a+bi a = -5 b = 5 you can plot a+bi on the complex number plane as the ordered pair (a,b) which is why satellite73 plotted the point (-5,5)
anonymous
  • anonymous
it means the angle is easy to find if you use arctangent here it will not work because you are in the wrong quadrant
jim_thompson5910
  • jim_thompson5910
http://img.sparknotes.com/figures/A/a28868a2f5deab01f6e8c7727c2ee7a4/complexplane.gif
anonymous
  • anonymous
if you took \(\tan^{-1}(-1)\) you get \(-\frac{\pi}{4}\) but you are not in quadrant 4, you are in quadrant 2
dumbsearch2
  • dumbsearch2
So it's 3pi/4 instead, right?
anonymous
  • anonymous
yes
anonymous
  • anonymous
you cannot use arctan unless you are in quadrant 1 or 4
jim_thompson5910
  • jim_thompson5910
well you can use arctan, just add on pi to get to the right quadrant
dumbsearch2
  • dumbsearch2
?
anonymous
  • anonymous
you have to either know it, or use \[\cos(\theta)=\frac{a}{r}\] and \[\sin(\theta)=\frac{b}{r}\]
jim_thompson5910
  • jim_thompson5910
as satellite73 said, arctan(-1) = -pi/4 add on pi to get to 3pi/4 (-pi/4) + (pi) = (-pi/4) + (4pi/4) = (-pi+4pi)/4 = 3pi/4
anonymous
  • anonymous
or what @jim_thompson5910 said, but in any case you have to know what quadrant you are in before you start

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