anonymous
  • anonymous
help :(
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
jhonyy9
  • jhonyy9
- so for point b. i think 45 degree
experimentX
  • experimentX
modulus = sqrt(3^2+3^2) = 3 sqrt(2) angle = 135 => arctan(-3/3)

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anonymous
  • anonymous
absolute values is the lenght which you get by pythagoras. for a complex number \(a+bi\) we have \(|a+bi|=\sqrt{a^b+b^2}\) in your case it is \[|-3+3i|=\sqrt{3^2+3^2}=\sqrt{18}=3\sqrt{2}\]
anonymous
  • anonymous
and the angle would be -45?
anonymous
  • anonymous
no and this is where you have to be careful!
anonymous
  • anonymous
it is true that \(\tan(\frac{b}{a})=\theta\) but it is not necessarily true that \(\theta=\tan^{-1}(\frac{b}{a})\)
anonymous
  • anonymous
you have to consider what quadrant you are in. arctan only returns values from -90 to 90, but from your picture you see that you are in quadrant II not in I or IV so you have to think what angle that is, it is not -45 but rather 135
.Sam.
  • .Sam.
|dw:1333292497661:dw|
anonymous
  • anonymous
you can also use in this case \(\tan^{-1}(\frac{b}{a})+180)\)
anonymous
  • anonymous
what .sam. said
anonymous
  • anonymous
thank you so much!

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