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satellite73Best ResponseYou've already chosen the best response.0
\[\sqrt{\frac{1i}{2}}\]?
 2 years ago

satellite73Best ResponseYou've already chosen the best response.0
where does the "30" go?
 2 years ago

Alexis1994_13Best ResponseYou've already chosen the best response.0
wait,I will use equation
 2 years ago

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

Alexis1994_13Best ResponseYou've already chosen the best response.0
\[[(\sqrt{2}(1i)/2 ]^{30}\]
 2 years ago

satellite73Best ResponseYou've already chosen the best response.0
\[(\frac{\sqrt{2}}{2}\frac{\sqrt{2}}{2}i)^{30}\]
 2 years ago

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

satellite73Best ResponseYou've already chosen the best response.0
makes the idea even easier than what was written
 2 years ago

satellite73Best ResponseYou've already chosen the best response.0
oh dear no my myininaya
 2 years ago

satellite73Best ResponseYou've already chosen the best response.0
i 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.
 2 years ago

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

Alexis1994_13Best ResponseYou've already chosen the best response.0
wrong answer,I need to found 1i. :S
 2 years ago

satellite73Best ResponseYou've already chosen the best response.0
ok do you know how to write this in polar form?
 2 years ago

satellite73Best ResponseYou've already chosen the best response.0
because once you do it is really easy
 2 years ago

satellite73Best ResponseYou've already chosen the best response.0
the number is \[\frac{\sqrt{2}}{2}\frac{\sqrt{2}}{2}i\]
 2 years ago

satellite73Best ResponseYou've already chosen the best response.0
which sits right on the unit circle
 2 years ago

satellite73Best ResponseYou've already chosen the best response.0
do you prefer degrees or radians for these?
 2 years ago

Alexis1994_13Best ResponseYou've already chosen the best response.0
The answer is 1i. But I don't know how to find it
 2 years ago

satellite73Best ResponseYou've already chosen the best response.0
actually that is not the answer, but we will find it. it is not hard
 2 years ago

satellite73Best ResponseYou've already chosen the best response.0
but before we begin, do you know how to write this in trigonometric form?
 2 years ago

Alexis1994_13Best ResponseYou've already chosen the best response.0
Do you mean A(root2/2,root2/2) ?
 2 years ago

satellite73Best ResponseYou've already chosen the best response.0
because 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
 2 years ago

satellite73Best ResponseYou've already chosen the best response.0
no i mean as \[r(\cos(\theta)+i\sin(\theta))\]
 2 years ago

satellite73Best ResponseYou've already chosen the best response.0
in this case \[r=1\] because we are right on the unit circle
 2 years ago

satellite73Best ResponseYou've already chosen the best response.0
\[\frac{\sqrt{2}}{2}\frac{\sqrt{2}}{2}i=1\]
 2 years ago

Alexis1994_13Best ResponseYou've already chosen the best response.0
I haven't learned anything like this yet.
 2 years ago

satellite73Best ResponseYou've already chosen the best response.0
so all we need it \[\theta\] which should be easy because we see these numbers all the time
 2 years ago

satellite73Best ResponseYou've already chosen the best response.0
well if you have not, you have no way to raise this to the power of 30!
 2 years ago

satellite73Best ResponseYou've already chosen the best response.0
i mean you are not expected to multiply this number by itself 30 times !
 2 years ago

Alexis1994_13Best ResponseYou've already chosen the best response.0
Wait,see what is extcally writes :
 2 years ago

satellite73Best ResponseYou've already chosen the best response.0
ok. but if you can write in trig from raising to the power of 30 is easy. maybe this is something else
 2 years ago

Alexis1994_13Best ResponseYou've already chosen the best response.0
u=(\[(\sqrt{2/2}\times w)^{30}\]
 2 years ago

Alexis1994_13Best ResponseYou've already chosen the best response.0
and we know that w=1i
 2 years ago

satellite73Best ResponseYou've already chosen the best response.0
yeah well that is what i wrote
 2 years ago

Alexis1994_13Best ResponseYou've already chosen the best response.0
The answer is i **
 2 years ago

satellite73Best ResponseYou've already chosen the best response.0
\[(\frac{\sqrt{2}}{2}(1i))^{30}\] like this yes?
 2 years ago

satellite73Best ResponseYou've already chosen the best response.0
well we can do it easily, but if you have not seen trig from i don't know how to explain it
 2 years ago

satellite73Best ResponseYou've already chosen the best response.0
i mean you certainly are not going to multiply this number by itself 30 times
 2 years ago

satellite73Best ResponseYou've already chosen the best response.0
ok this number is \[\frac{\sqrt{2}}{2}\frac{\sqrt{2}}{2}i\] \[=\cos(\frac{7\pi}{4})+i\sin(\frac{7\pi}{4})\]
 2 years ago

Alexis1994_13Best ResponseYou've already chosen the best response.0
I have an idea. We can do this: (\frac{\sqrt{2}}{2}(1i))^{29}*\frac{\sqrt{2}}{2}
 2 years ago

satellite73Best ResponseYou've already chosen the best response.0
so when you raise to the power of 30 you just multiply the angle by 30
 2 years ago

Alexis1994_13Best ResponseYou've already chosen the best response.0
I have an idea. We can do this: (\frac{\sqrt{2}}{2}(1i))^{29}*(\frac{\sqrt{2}}{2}(1i)
 2 years ago

satellite73Best ResponseYou've already chosen the best response.0
\[(\frac{\sqrt{2}}{2}(1i))^{29}*\frac{\sqrt{2}}{2}(1i)\]
 2 years ago

satellite73Best ResponseYou've already chosen the best response.0
ok that is what you wrote yes?
 2 years ago

Alexis1994_13Best ResponseYou've already chosen the best response.0
*(\[\sqrt{2}/2+\sqrt{2}/2\]
 2 years ago

satellite73Best ResponseYou've already chosen the best response.0
ok 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 \[i\]
 2 years ago

satellite73Best ResponseYou've already chosen the best response.0
without polar form or trig form i really don't know how you are expected to do this problem.
 2 years ago

satellite73Best ResponseYou've already chosen the best response.0
sorry that was not much help.
 2 years ago

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

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

satellite73Best ResponseYou've already chosen the best response.0
actually i am not kicking myself yet
 2 years ago

satellite73Best ResponseYou've already chosen the best response.0
since this is wrong
 2 years ago

satellite73Best ResponseYou've already chosen the best response.0
oh wait. i was looking at the first line.
 2 years ago

satellite73Best ResponseYou've already chosen the best response.0
but you are right it must be a "typo"
 2 years ago

satellite73Best ResponseYou've already chosen the best response.0
you do get \[(1i)(1i)=2i\]
 2 years ago

satellite73Best ResponseYou've already chosen the best response.0
everything looks good but your answer!
 2 years ago

satellite73Best ResponseYou've already chosen the best response.0
because i happen to know that it is i, not 1
 2 years ago

myininayaBest ResponseYou've already chosen the best response.1
i will look at it again
 2 years ago

myininayaBest ResponseYou've already chosen the best response.1
but the approach looks good
 2 years ago

satellite73Best ResponseYou've already chosen the best response.0
taht is ok you just forgot the \[i^{15}\] in your answer
 2 years ago

satellite73Best ResponseYou've already chosen the best response.0
no it is right, you just forgot one part i think at the end. much much easier in polar form really
 2 years ago

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

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