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anonymous
 5 years ago
express in polar form r cisθ for:
a) 1i
b) 3+4i (to 2 decimal places of a degree)
c) use your answers to parts a) and b) to simplify (3+4i)/(1i)^2 in polar form.
anonymous
 5 years ago
express in polar form r cisθ for: a) 1i b) 3+4i (to 2 decimal places of a degree) c) use your answers to parts a) and b) to simplify (3+4i)/(1i)^2 in polar form.

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0first you need \[r=\sqrt{a^2+b^2}\] so for part a you get \[r=\sqrt{2}\] and for part b you get \[r=5\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0then you need \[\theta\] which you get by solving \[tan(\frac{b}{a})=\theta\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0are you using degree or radians for this? if radians the first one is \[\frac{5\pi}{4}\] if degrees is it 225

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0if you plot 1i you see you are in quadrant III which is why you get 225

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0for part b you get \[tan^{1}(\frac{4}{3})\] from a calculator then you have to add 180 to your answer. let me see if i have one

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i get 126.78 to two places but you should check it

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0so answer to first one is \[\sqrt{2}(cos(45)+isin(45))\] and second is \[5(cos(126.78)+isin(126.78))\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0then to divide, you divide the r's and subtract the angles.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0what does it say next to (45)? its all blurry. thanks for your help so far!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0ok first of all i made a mistake. it is not 45 it should be 225

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i don't know why i wrote 45 because earlier i said the angle is 225 degrees

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0it says cos(225)+isin(225)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0i guess the latex is hard to read but may be clearer if you refresh the browser, that often works for me

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0oh thanks for the tip!

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0your next job is to square \[(1i)\] which is actually very easy not in polar form, but i guess they want it in polar form so we do it

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0you do it by squaring r and doubling the angle so you get \[(1i)^2=\sqrt{2}^2(cos(225\times 2)+isin(225\times2))\] \[=2cos(450)+isin(450))\] \[=2(cos(90)+isin(90))\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0the last equality because sine and cosine are periodic with period 360 so i just subtracted 360 from 450 to get 90

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0btw this problem is really stupid because \[(1i)^2\] is just 2i and dividing by 2i is easy. very annoying to put in polar form. but in any case we see that since cos(90)=0 and sin(90)=1 we get \[(1i)^2=2i\] using polar form

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0your last job is to divide. as i said dividing by 2i is easy but they want you to use polar form so you divide 5 by 2 and subtract 90 from 126.78 to get the answer of \[\frac{5}{2}(cos(36.78)+isin(36.78))\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0now the snap way: \[\frac{3+4i}{(1i)^2}=\frac{3+4i}{2i}\] \[=\frac{3+4i}{2i}\times \frac{i}{i}=\frac{4+3i}{2}=2+\frac{3}{2}i\]\]

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0thank you that answer matches the answer in the book :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0good. hope you understood the steps and that dividing by 2i is much easier without converting to polar for. easy to divide!
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