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FP1 - complex numbers question

Guys, I came across this question and wondered how I'd go about doing it,

The square root of 'i' can be written in the forum a+bi
Find a and b.

Help would be very much appreciated.
Reply 1
Avatar for ubisoft
ubisoft
3
(a+ib)2=i(a+ib)^2 = i

a2+2abi−b2=ia^2 +2abi -b^2 =i

a2−b2=0[br]thereforea=ba^2 - b^2 = 0[br] therefore a = b

2ab=1[br]ab=1/22ab = 1[br]ab = 1/2

a and b =12 \frac{1}{\sqrt2}

Answer: 12+12i \frac{1}{\sqrt2}+ \frac{1}{\sqrt2}i
(edited 9 years ago)
Original post by WinterApproaches
Guys, I came across this question and wondered how I'd go about doing it,

The square root of 'i' can be written in the forum a+bi
Find a and b.

Help would be very much appreciated.

I can't remember how to do this from FP1 sorry

but Google is your best friend use it :smile:

http://www.google.co.uk/search?q=square+root+of+i&oq=square+root+of+i

https://www.math.toronto.edu/mathnet/questionCorner/rootofi.html
Original post by WinterApproaches
Guys, I came across this question and wondered how I'd go about doing it,

The square root of 'i' can be written in the forum a+bi
Find a and b.

Help would be very much appreciated.


I would start off by saying defining the square root of i to be a new number, z where z=a+biz=a+bi.
Then we are trying to solve: i=z2=(a+bi)2i=z^{2}=(a+bi)^{2}

Now you can maybe solve it from here? You will get two simultaneous equations to solve.


Alternatively, if you have learned this notation before:
Can you use these two facts together to try and get the answer:
i=e(iπ2)=cos(π2)+isin(iπ2)i=e^{\left ( \frac{i \pi }{2}\right )}=cos\left ( \frac{\pi }{2}\right )+isin\left ( \frac{i \pi }{2}\right )
i=i12\sqrt{i}=i^{\frac{1}{2}}

Original post by ubisoft
12+12i\frac{1}{\sqrt2} + \frac{1}{\sqrt2}i

That's not really helpful. -_-
And your edit just posts the answer - this is against the rules.
Reply 4
Avatar for ubisoft
ubisoft
3
Original post by rayquaza17


That's not really helpful. -_-
And your edit just posts the answer - this is against the rules.


Sorry, I'm trying to figure out how this latex stuff works, I'm new to it.
Original post by ubisoft
Sorry, I'm trying to figure out how this latex stuff works, I'm new to it.


It's okay. I'm not very good either, but I use this link to help: http://www.codecogs.com/latex/eqneditor.php

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