Negative under the square root (1 Viewer)

[physician]

I havnt done 4 unit maths before, But i was wondering

could someone possibly explain what happens (in 4 unit) when u obtain a negative under the square root???... or possibly explain why its defined in 4 unit but undefined in 2 and 3 unit!!!

Im just interested as there was a calculation I was doing, and found that i obtained a negative under the square root... I was wondering where i could go from there???

 

[KFunk]

Well we define i such that: i² = -1 or, alternatively, i = √(-1) ... that's about it really. Takes you into the complex number system.

 

[Templar]

When you have a negative under the square root in ext 2, you resolve it to complex numbers since it is part of the syllabus. However complex numbers are not part of the maths or ext 1 syllabus, hence square roots of negative numbers are undefined.

You use sqrt(-1)=i and work it from there.

 

[icycloud]

To put it very simply, a new constant "i" is introduced, and is defined as:

i = Sqrt[-1]

So to evaluate something like Sqrt[-64]:

Sqrt[-64] = Sqrt[-1] * Sqrt[64] = 8i

 

[physician]

WOW, thanks for the quick replies!

ok,

well this is the value i got in my calculation

Sqrt ( - 1.200668062 * 10²⁸ )

hehe, yes! a very huge number!

so does that become:

Sqrt ( 1.200668062 * 10²⁸ )*i ?

 

[physician]

oh I forgot...

complex numbers.. so what happens to i?

sorry dudes....

but geeeez, 4 unit sounds interesting and Fun!

 

[Trev]

√(-a)
√(ai²)
i√a