Easy qn (1 Viewer)

[Richard Lee]

There are two questions; find the square roots of 3+4i and find sqrt(3+4i). Do u think the solutions are same?

 

[ND]

edit: i should probably leave these questions for the '04ers...

 

[ae]

yes

 

[sven0023]

hmm ill give it a go

1)

sqr/(3+4i) = x+iy
3+4i = (x+iy)^2
= x^2-y^2+2ixy

Equating real/non real, 3 = x^2-y^2 and y = 2/x

Sub y = 2/x in, 3 = x^2 - (2/x)^2
3x^2 = x^4 - 4
x^4 - 3x^2 - 4 = 0
(x^2-4)(x^2+1) = 0
x^2 = 4
x = +/- 2
y = +/- 1

Therefore, sqr/(3+4i) = 2+i or -2-i


2) is sqr/(3+4i) just the positive values?? ie 2+i

 

[turtle_2468]

There's no such thing as a "positive" square root in complex numbers...
ie the square root symbol in reals implies the positive one, but there's no satisfactory way to imply positiveness in complex, so ppl just write both...

 

[Richard Lee]

Thanks! So, sqrt(-1) should be (+/-)i.

 

[Richard Lee]

Originally posted by turtle_2468
There's no such thing as a "positive" square root in complex numbers...
ie the square root symbol in reals implies the positive one, but there's no satisfactory way to imply positiveness in complex, so ppl just write both...

Good! So, sqrt(4+0i)=(+/-)(2+0i) and sqrt(4)=2.
I think I know what you mean.

 

[freaking_out]

Originally posted by ND
edit: i should probably leave these questions for the '04ers...

lol, u prolly answered it instinctively- and then u realised.

 

[KeypadSDM]

Originally posted by Richard Lee
Good! So, sqrt(4+0i)=(+/-)(2+0i) and sqrt(4)=2.
I think I know what you mean.

Actually that's a misinterpretation.

Square roots of complex numbers can't be identified as either positive or negative.

An example: - 3 + 4i OR 3 - 4i

Which is positive, which is negative? Neither has a right to either title, hence the ambiguity.

If the unreal part is zero, then the number is real. sqrt(real) is always positive.

 

[spice girl]

in fact i remember chucking a fuss about it in jr high. cos the teacher taught that sqrt(n) meant the number(s) that when squared would give the number n. So to answer sqrt(4) i'd say +/-2. But then *NO*, the teacher says it's only the positive value, and i ask why, and he goes cos there's no negative sign behind it. and i thought "BS! wot an ignorant sweeping assumption"

bleh