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hartnn
 one year ago
Best ResponseYou've already chosen the best response.2do you know how to convert the form a+bi into polar form, r <theta ?

sedighn
 one year ago
Best ResponseYou've already chosen the best response.0Yes I do... I've never seen such a question so I'm not sure how to begin!

hartnn
 one year ago
Best ResponseYou've already chosen the best response.2convert 5+2i into polar first

sedighn
 one year ago
Best ResponseYou've already chosen the best response.0okay so... \[\left[ \sqrt{29},0.381 \right]\]

dumbcow
 one year ago
Best ResponseYou've already chosen the best response.0\[\sqrt{r(\cos \theta +i \sin \theta)} = \sqrt{r}(\cos \frac{\theta}{2} +i \sin \frac{\theta}{2})\]

hartnn
 one year ago
Best ResponseYou've already chosen the best response.2so just take square root of r half the angle and then convert it back to a+bi form

sedighn
 one year ago
Best ResponseYou've already chosen the best response.0wow okay thanks a lot! we didn't do this method in class o.o

hartnn
 one year ago
Best ResponseYou've already chosen the best response.2well, now you are smarter than your classmates ;) (Y)

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1There's an alternative way if you're interested

hartnn
 one year ago
Best ResponseYou've already chosen the best response.2sure ! @jim_thompson5910

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1it only works for square roots though

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1Alternative Way: Let z = a+bi z = a+bi z^2 = (a+bi)(a+bi) z^2 = a^2 + 2ab*i + bi^2 z^2 = a^2 + 2ab*i + b^2(1) z^2 = a^2 + 2ab*i  b^2 z^2 = a^2  b^2 + 2ab*i z^2 = (a^2  b^2) + (2ab)*i So if z = a+bi, then z^2 = (a^2  b^2) + (2ab)*i The real part of z^2 is a^2  b^2 and the imaginary part of z^2 is 2ab  The idea is that if z = a+bi is a square root of some complex number w, then z^2 = w Now let w = 5+2i z^2 = w z^2 = 5+2i (a^2  b^2) + (2ab)*i = 5+2i The real part of 5+2i is 5, so a^2  b^2 = 5 The imaginary part of 5+2i is 2, so 2ab = 2  You now have these two equations a^2  b^2 = 5 2ab = 2 with 2 unknowns. You can use these two equations together (with the use of substitution) to solve for 'a' and 'b'

sedighn
 one year ago
Best ResponseYou've already chosen the best response.0I seee... thanks heaps

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.1you're welcome
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