...Despite another over worked day.

And another complex day.

I got into a very heated aguement...Oh sorry...debate - 90534
It's not surpising really...that I'm a determinismist. We are all determined to die...To be honset; as a learning mathematican...Seeking a gernal law for everything...
You see, we don't have free will.
I'm willing to argue that agian...for anyone sake.

Anyway...You deserve much better. Leaving you worry....and scared...and angry.
Perhaps you should do the same to him...
ahh...You remembered about my pen! <3 style="font-style: italic;">And it's been a while since I threw in some maths...Have fun.

Work out the Sqrt of 3+4i

Supposing the square root of 3+4i is a+ib where a and b is real

Then

(a+ib)²=3 + 4i

(a+ib) (a+ib) = 3 + 4i

a(a+ib) + ib(a+ib) = 3 + 4i

a² + abi + abi – b² = 3+4i

(a²-b²) +2abi = 3+4i

By equating the real parts from each side of the equation, and the imaginary parts too.

I a² – b² =3

II 2ab =4

4/2a =2/a

Substituing into i a²-4/a² =3

A⁴ – 4 = 3a²

A⁴ -3a² – 4 =0

(a² – 4)(a² + 1) = 0

Therefore a² = 4 or -1

Since we supposed a is to be real, a² cannot be -1

Solutions are a =2 or a = -2

Substituting back into b=2/a

When a =2 b =1

When a = -2 b = -1

Therefore the sqrt is 2 +i and -2 -i

God...I feel so bored and alone...
What free will? It's just an illusion...