anonymous
  • anonymous
Express the complex number in trigonometric form. -3i
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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jim_thompson5910
  • jim_thompson5910
Think of `-3i` as `0-3i = 0 + (-3i)` the last expression is in the form `a+bi` where `a = 0` and `b = -3`
jim_thompson5910
  • jim_thompson5910
You need to find r and theta use \[\Large r = \sqrt{a^2 + b^2}\] \[\Large \theta = \arctan\left(\frac{b}{a}\right)\]
anonymous
  • anonymous
r = √0^2 + -3^2 = √0 + 9 = √9 = 3

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jim_thompson5910
  • jim_thompson5910
yep `r = 3`
jim_thompson5910
  • jim_thompson5910
basically that says: "the point (0,-3) is 3 units away from the origin" `0+(-3i)` can be plotted on the complex plane as the point (0,-3)
jim_thompson5910
  • jim_thompson5910
what would theta be?
anonymous
  • anonymous
im getting an error for theta..
jim_thompson5910
  • jim_thompson5910
yes you'll find that b/a = -3/0 = undefined where is tangent undefined?
anonymous
  • anonymous
cos(x) = 0 ?
jim_thompson5910
  • jim_thompson5910
I guess a better way to find theta is by plotting where 0-3i is located |dw:1442705686511:dw|
jim_thompson5910
  • jim_thompson5910
what angle is this? |dw:1442705720789:dw|
anonymous
  • anonymous
270 ?
jim_thompson5910
  • jim_thompson5910
yes
jim_thompson5910
  • jim_thompson5910
r = 3 and theta = 270, we now plug those values into \[\Large r\left[\cos(\theta)+i*\sin(\theta)\right]\]
jim_thompson5910
  • jim_thompson5910
|dw:1442705859091:dw|
anonymous
  • anonymous
3(cos 270 + i sin 270) ?
jim_thompson5910
  • jim_thompson5910
correct
Plasmataco
  • Plasmataco
yay

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