Hard Root of Complex Number (1 Viewer)

[RealiseSomethin]

lol hard root..

 

[largarithmic]

Isn't it just plus or minus the square root of the modulus times cis(theta) where theta is half the argument? That seems like a much more simplistic way considering the argument is so clean.

its usually very unclean... for instance, in the example (12 - 6i) the value of the argument is -tan^(-1) [2], which you'd be struggling to find any sort of nice form for - you can plug it in your calculator, halve it and find the cartesian form of the square root but either you're going to have an answer in terms of tan^-1 stuff, or one in the decimal form your calculator puts it in, neither of which I think are usually accepted as answers. You could do it by solving to find sin(theta/2) and cos(theta/2) from the quadratic equations you get from the double angle formulae, but thats effectively the same thing as doing it the way slyhunter did

 

[lolcakes52]

Isn't the value of the argument -pi/4? That isn't difficult. The Square root is plus or minus the fourth root of 180 times cis -pi/8. Relatively simple considering the alternative solution given.

 

[D94]

Isn't the value of the argument -pi/4? That isn't difficult. The Square root is plus or minus the fourth root of 180 times cis -pi/8. Relatively simple considering the alternative solution given.

No.... Tan@=y/x so it's -0.5

 

[lolcakes52]

No.... Tan@=y/x so it's -0.5

No, tan@=-0.5, therefore @=pi/4. When you find the square root, you divide the argument by 2, Hence @=-pi/8.

 

[D94]

No, tan@=-0.5, therefore @=pi/4. When you find the square root, you divide the argument by 2, Hence @=-pi/8.

Erm...how the hell does = ? ..... It doesn't; check with your calculator.

 

[Carrotsticks]

From where did you get this question? I'm curious as to what kind of textbook would give you a question with a solution so ugly.

 

[D94]

From where did you get this question? I'm curious as to what kind of textbook would give you a question with a solution so ugly.

From memory, I think it's a Patel question. A few answers are just the argument left as an arctan, and not really give you a proper answer.

 

[lolcakes52]

Erm...how the hell does = ? ..... It doesn't; check with your calculator.

My bad, got confused with sin(45). Im an idiot.

 

[Carrotsticks]

lol either way, sin45 = 1/sqrt2, not -0.5

 

[lolcakes52]

lol either way, sin45 = 1/sqrt2, not -0.5

Its a bad dyslexia day.

 

[Siddy123]

Its a bad dyslexia day.

LMAAOOOOO
we all have them here and there

 

[Nooblet94]

Do you realise you just replied to a post that's 2.5 months old..?