Unclear resolution (imaginary number equation) | Mathematics | Page 1

abstract foxBOT Jan 20, 2025, 10:41 PM

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radiant zealot Jan 20, 2025, 10:49 PM

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how?

soft dagger Jan 20, 2025, 10:53 PM

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euler formula

radiant zealot Jan 20, 2025, 10:56 PM

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soft dagger euler formula

?

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I don't get what happens past like

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Splitting the equation into Z and the stuff in the brackets

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Why is it 3π/2?

soft dagger Jan 20, 2025, 10:57 PM

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euler formula says: e^ip = cos(p)+isin(p) <=> -3i = cos(3pi/2)+isin(3pi/2) = e^i3pi/2

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p is an angle

radiant zealot Jan 20, 2025, 10:58 PM

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what the heeeeeelll

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thank you

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clearly this exercise wasn't meant for me

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we've never touched on that in class

soft dagger Jan 20, 2025, 10:59 PM

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you can also solve it by assuming z can be written in the form of z = x+yi and then find the values for x and y

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but euler is faster and easier

radiant zealot Jan 20, 2025, 10:59 PM

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I tried that and the answer was different

soft dagger Jan 20, 2025, 10:59 PM

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can you show me what you did?

radiant zealot Jan 20, 2025, 10:59 PM

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sure

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Its a little shaky though giv me. A second to rewrite it

soft dagger Jan 20, 2025, 10:59 PM

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aight np

radiant zealot Jan 20, 2025, 11:03 PM

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soft dagger aight np

rn_image_picker_lib_temp_e4fbf1a1-862f-493d-9d84-2340e28f774f.jpg

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we do a+bi

soft dagger Jan 20, 2025, 11:04 PM

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u can use |a+bi| = a^2+b^2 btw

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so a+bi = -3i => |a+bi| = |-3i| => a^2+b^2 = 9

radiant zealot Jan 20, 2025, 11:05 PM

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Im lost

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The 9 is the real part

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But there is no 9

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Where'd it come from

soft dagger Jan 20, 2025, 11:06 PM

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radiant zealot Im lost

are you aware that |a+bi| = (a^2+b^2)^0.5

radiant zealot Jan 20, 2025, 11:09 PM

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no

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right it seems this really is out of my league

soft dagger Jan 20, 2025, 11:10 PM

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think about a circle, where y axis is the imaginary numbers and x axis is for reel numbers. Now how would you calculate the length from origo to a value a+bi in this circle?

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for example, if you have the point x=3, and y=2 and you drew a line from origo to the point. How would you calculate the length of this line?

radiant zealot Jan 20, 2025, 11:11 PM

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a^2 + b^2

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Root of that anyways

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So root of 13

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mhm

soft dagger Jan 20, 2025, 11:11 PM

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pythagoros ye. You can apply the same strategy with imaginary numbers

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so then you have that a^2+b^2 = 9 and a^2-b^2 = 0

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so you can calculate a

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and then you can calculate b using your other equation

radiant zealot Jan 20, 2025, 11:12 PM

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soft dagger so then you have that a^2+b^2 = 9 and a^2-b^2 = 0

Why is the negative one equal 0

soft dagger Jan 20, 2025, 11:12 PM

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radiant zealot

because of this

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you've already written that equation

radiant zealot Jan 20, 2025, 11:13 PM

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Cuz they're equal?

soft dagger Jan 20, 2025, 11:13 PM

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cus theres no reel numbers in this equation

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so it must be 0

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and 2ab = -3

radiant zealot Jan 20, 2025, 11:14 PM

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Yeah I got that part

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hm

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Ok I see

radiant zealot Jan 20, 2025, 11:15 PM

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soft dagger so you can calculate a

So where are we left with this

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A is square root of 9?

soft dagger Jan 20, 2025, 11:17 PM

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2a^2 = 9

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a is square root of 9/2

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+- ofc

radiant zealot Jan 20, 2025, 11:17 PM

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But then isn't b the same

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hm

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I'm sorry I'm too tired to actually process any of thus

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I'll save this conversation then look at this tomorrow

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Ar this point I have the tools to reply by myaelf

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If it's just distance equations and the like

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Thank you for your help

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Nevertheless the official resolution uses eullers something or other

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Which we definitely didn't atudy

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But that doesn't concern you

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Thanks

#Unclear resolution (imaginary number equation)