# Square root of a complex number!



## Wildsoldier PE (Sep 14, 2011)

Does anyone knows how to get the square root of a complex number?

For example if i want the square root of (23+40i), the Casio FX115 ES and MS gives me a math error. If i use the TI-92plus which is not allowed for the exam gives me the correct answer without problems.

Any ideas?


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## Flyer_PE (Sep 14, 2011)

Convert it to polar. Take the square root of the magnitude. Divide the angle in half. Convert back to rectangular.

I get 5.88+j3.40.


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## EEVA PE (Sep 14, 2011)

Wildsoldier said:


> Does anyone knows how to get the square root of a complex number?
> For example if i want the square root of (23+40i), the Casio FX115 ES and MS gives me a math error. If i use the TI-92plus which is not allowed for the exam gives me the correct answer without problems.
> 
> Any ideas?



I get 4.197501899 using a Casio fx-115ES. I did shift - 2 3 shift ) 4 0 ) = sqrt Ans

Compare my answer to what you got on the TI-92, was it the same?

It must be wrong since I lost the imaginary number somewhere.

Looks like Flyer has the right method.


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## Wildsoldier PE (Sep 14, 2011)

Thanks i'm going to check when i get back home. I'm at work right now and i dont have the TI here to check. That number that i put was an example!



EEVA said:


> Wildsoldier said:
> 
> 
> > Does anyone knows how to get the square root of a complex number?
> ...


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## petobe-gw (Sep 15, 2011)

Flyer_PE said:


> Convert it to polar. Take the square root of the magnitude. Divide the angle in half. Convert back to rectangular.
> I get 5.88+j3.40.


this is correct. I followed Flyer's directions on my Casio fx-115ES and double checked it with my HP48G and get the same answer, 5.88 + j3.40.

arty-smiley-048:


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## Wildsoldier PE (Sep 15, 2011)

petobe-gw said:


> Flyer_PE said:
> 
> 
> > Convert it to polar. Take the square root of the magnitude. Divide the angle in half. Convert back to rectangular.
> ...



Yup is correct i checked at home at gives the right answer. Thanks Flyer PE


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## Jonjo (Sep 19, 2011)

Wildsoldier said:


> Does anyone knows how to get the square root of a complex number?
> For example if i want the square root of (23+40i), the Casio FX115 ES and MS gives me a math error. If i use the TI-92plus which is not allowed for the exam gives me the correct answer without problems.
> 
> Any ideas?


Wildsoldeir : Just apply "de Moivre theorem" , look at your Math book (Trig) , here is the link in wikipedia ,

http://en.wikipedia.org/wiki/De_Moivre%27s_formula

Jonjo


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