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Find All Solutions of Squareroot of 2i

Isn't it impossible to get the square root of a negative number?

(Unless I just haven't reached that part of my A level course yet - in which case, I apologise. )

edit - might be wrong actually, credit to james for pointing out differences with complex numbers

looking at a few sites, the principal square root is defined as the root with a non negative real part but this formula seems to break down for negative reals

But the square root of a number is always +-
I think you're incorrect

(Original post by PILEDRIV3R WALTZ)
But the square root of a number is always +-
I think you're incorrect

y^2=x is not teh same as y=\sqrt{x}

Actually it is a bit different with complex numbers.

For complex numbers the square root function can mean several different (infiinite) things, you first have to define it (there are only really 2 sensible choices, all the others aren't even continuous).

If you want to solve x^2+4=0 then both are solutions, but just using the square root sign doesn't make sense on its own.

(Original post by james22)
Actually it is a bit different with complex numbers.

For complex numbers the square root function can mean several different (infiinite) things, you first have to define it (there are only really 2 sensible choices, all the others aren't even continuous).

If you want to solve x^2+4=0 then both are solutions, but just using the square root sign doesn't make sense on its own.

Thank god someone agrees with me that the answer is +- 2i

(Original post by PILEDRIV3R WALTZ)
Thank god someone agrees with me that the answer is +- 2i

Except that I don't. The answer could be either, but it is certainly not both.

(Original post by james22)
Except that I don't. The answer could be either, but it is certainly not both.

How can it be either? You're clearly a newbie to Maths and algebra

(Original post by PILEDRIV3R WALTZ)
How can it be either? You're clearly a newbie to Maths and algebra

It can be either because, until you have define what you mean by the square root function, it doesn't make sense. One definition will give 2i, another will give -2i.

(Original post by james22)
It can be either because, until you have define what you mean by the square root function, it doesn't make sense. One definition will give 2i, another will give -2i.

Did you go to London metropolitan by any chance?

(Original post by PILEDRIV3R WALTZ)
Did you go to London metropolitan by any chance?

Now I am certain you are a troll and not just really bad at maths, so I won't waste any more time trying to explain this.

(Original post by Arithmeticae)
edit - might be wrong actually, credit to james for pointing out differences with complex numbers

looking at a few sites, the principal square root is defined as the root with a non negative real part but this formula seems to break down for negative reals

I have nothing more to add other than how amazing your profile pic is

oi oi I thought you had an A* in Further maths according to your post on another thread. Slacking mate

2i? Does that mean 4 = 2 clones of me?

Find All Solutions of Squareroot of 2i

Source: https://www.thestudentroom.co.uk/showthread.php?t=2914941