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Alexis1994_13
 3 years ago
u=[root2(1i)/2]30
Find the number u.
Alexis1994_13
 3 years ago
u=[root2(1i)/2]30 Find the number u.

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satellite73
 3 years ago
Best ResponseYou've already chosen the best response.0\[\sqrt{\frac{1i}{2}}\]?

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.0where does the "30" go?

Alexis1994_13
 3 years ago
Best ResponseYou've already chosen the best response.0wait,I will use equation

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.1u=\[\sqrt{\frac{(1i)}{2}}*30\]

Alexis1994_13
 3 years ago
Best ResponseYou've already chosen the best response.0\[[(\sqrt{2}(1i)/2 ]^{30}\]

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.0\[(\frac{\sqrt{2}}{2}\frac{\sqrt{2}}{2}i)^{30}\]

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.1\[2^\frac{30}{2}*\frac{(1i)^{30}}{2^{30}}=2^{15}*\frac{(1i)^{30}}{2^{30}}=\frac{(1i)^{30}}{2^{15}}\]

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.0makes the idea even easier than what was written

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.0oh dear no my myininaya

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.0i bet it is what i wrote, because that is an easy one. rewrite in trig (polar, whatever) form. then multiply the angle by 30. the modulus (absolute value) is 1 so nothing to worry about since you are on the unit circle.

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.1leave me alone i don't know math

Alexis1994_13
 3 years ago
Best ResponseYou've already chosen the best response.0wrong answer,I need to found 1i. :S

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.0ok do you know how to write this in polar form?

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.0because once you do it is really easy

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.0the number is \[\frac{\sqrt{2}}{2}\frac{\sqrt{2}}{2}i\]

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.0which sits right on the unit circle

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.0do you prefer degrees or radians for these?

Alexis1994_13
 3 years ago
Best ResponseYou've already chosen the best response.0The answer is 1i. But I don't know how to find it

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.0actually that is not the answer, but we will find it. it is not hard

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.0but before we begin, do you know how to write this in trigonometric form?

Alexis1994_13
 3 years ago
Best ResponseYou've already chosen the best response.0Do you mean A(root2/2,root2/2) ?

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.0because the idea is just to multiply the angle by 30 and see what you get. the absolute value of this number is 1, and 1 to the power of 30 is 1

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.0no i mean as \[r(\cos(\theta)+i\sin(\theta))\]

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.0in this case \[r=1\] because we are right on the unit circle

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.0\[\frac{\sqrt{2}}{2}\frac{\sqrt{2}}{2}i=1\]

Alexis1994_13
 3 years ago
Best ResponseYou've already chosen the best response.0I haven't learned anything like this yet.

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.0so all we need it \[\theta\] which should be easy because we see these numbers all the time

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.0well if you have not, you have no way to raise this to the power of 30!

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.0i mean you are not expected to multiply this number by itself 30 times !

Alexis1994_13
 3 years ago
Best ResponseYou've already chosen the best response.0Wait,see what is extcally writes :

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.0ok. but if you can write in trig from raising to the power of 30 is easy. maybe this is something else

Alexis1994_13
 3 years ago
Best ResponseYou've already chosen the best response.0u=(\[(\sqrt{2/2}\times w)^{30}\]

Alexis1994_13
 3 years ago
Best ResponseYou've already chosen the best response.0and we know that w=1i

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.0yeah well that is what i wrote

Alexis1994_13
 3 years ago
Best ResponseYou've already chosen the best response.0The answer is i **

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.0\[(\frac{\sqrt{2}}{2}(1i))^{30}\] like this yes?

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.0well we can do it easily, but if you have not seen trig from i don't know how to explain it

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.0i mean you certainly are not going to multiply this number by itself 30 times

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.0ok this number is \[\frac{\sqrt{2}}{2}\frac{\sqrt{2}}{2}i\] \[=\cos(\frac{7\pi}{4})+i\sin(\frac{7\pi}{4})\]

Alexis1994_13
 3 years ago
Best ResponseYou've already chosen the best response.0I have an idea. We can do this: (\frac{\sqrt{2}}{2}(1i))^{29}*\frac{\sqrt{2}}{2}

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.0so when you raise to the power of 30 you just multiply the angle by 30

Alexis1994_13
 3 years ago
Best ResponseYou've already chosen the best response.0I have an idea. We can do this: (\frac{\sqrt{2}}{2}(1i))^{29}*(\frac{\sqrt{2}}{2}(1i)

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.0\[(\frac{\sqrt{2}}{2}(1i))^{29}*\frac{\sqrt{2}}{2}(1i)\]

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.0ok that is what you wrote yes?

Alexis1994_13
 3 years ago
Best ResponseYou've already chosen the best response.0*(\[\sqrt{2}/2+\sqrt{2}/2\]

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.0ok you have to write \[\frac{7\pi}{4}\times 30=\frac{105\pi}{2}\] and realize that this is the same place on the unit circle as \[\frac{\pi}{2}\] and so the answer is \[i\]

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.0without polar form or trig form i really don't know how you are expected to do this problem.

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.0sorry that was not much help.

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.1omg you guys made this totally harder than is should be \[(1i)*(1i)=12ii^2=12i(1)=12i+1=2i\] \[(1i)^2=2i\] \[(1i)^{2*15}=(2i)^{15}\] \[(1i)^{30}=(2i)^{15}\] \[(1i)^{30}=(2)^{15}i^{15}=2^{15}i^{4*3+2}=2^{15}i^2=2^{15}(1)=2^{15}\] \[(1i)^{30}=2^{15}\] \[(\frac{\sqrt{2}}{2}(1i))^{30}=\frac{2^{15}}{2^{30}}(1i)^{30}=\frac{1}{2^{15}}*2^{15}=1\]

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.1i made a typo in first line \[(1i)(1i)=12i+i^2=12i+(1)=2i\]

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.0actually i am not kicking myself yet

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.0since this is wrong

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.0oh wait. i was looking at the first line.

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.0but you are right it must be a "typo"

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.0you do get \[(1i)(1i)=2i\]

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.0everything looks good but your answer!

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.0because i happen to know that it is i, not 1

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.1i will look at it again

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.1but the approach looks good

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.0taht is ok you just forgot the \[i^{15}\] in your answer

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.0no it is right, you just forgot one part i think at the end. much much easier in polar form really

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.1\[i^{4*3+3}\] omg i put a 2 where that 3 was

myininaya
 3 years ago
Best ResponseYou've already chosen the best response.1did you see my mistake above \[(2)^{15}*i^{15}=2^{15}*i^{4*3+3}=2^{15}*i^3=2^{15}*(i)=2^{15}*i\] \[\frac{1}{2^{15}}*(1i)^{30}=\frac{1}{2^{15}}*(2^{15}*i)=i\]
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