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# (-1)^(1/2) ???? error

0
748
4

Why can't I take (-1)^1/2

Nov 4, 2015

#2
+10

Why can't I take (-1)^1/2

This means

$$\sqrt{-1}$$

Now

$$\sqrt{25}=5\\ because\;\; 5*5 = 25\\ so\\ think\;\;about\;\; \sqrt{any\;negative\;number}$$

a positive * a positive = a positive

a negative * a negative = a positive

Mmm

you cannot multiply any real number by itself and get a negative answer.  That is impossible !!

So

$$\sqrt{-1}$$

has no real solution!!!

That is why you cannot do it!!

$$\sqrt{-1}$$

is the basis of the imaginary number system.  It is called i (or sometimes j)

$$i=\sqrt{-1}$$

.
Nov 4, 2015

#1
0

Try (-1)*-0.5

Nov 4, 2015
#2
+10

Why can't I take (-1)^1/2

This means

$$\sqrt{-1}$$

Now

$$\sqrt{25}=5\\ because\;\; 5*5 = 25\\ so\\ think\;\;about\;\; \sqrt{any\;negative\;number}$$

a positive * a positive = a positive

a negative * a negative = a positive

Mmm

you cannot multiply any real number by itself and get a negative answer.  That is impossible !!

So

$$\sqrt{-1}$$

has no real solution!!!

That is why you cannot do it!!

$$\sqrt{-1}$$

is the basis of the imaginary number system.  It is called i (or sometimes j)

$$i=\sqrt{-1}$$

Melody Nov 4, 2015
#3
0

Okay super I understand, but what about $${(-1)}^{1/3}$$

I think that will be $$\sqrt{-1}$$

You can say (-1)*(-1)*(-1) = -1, but it still says error?

Nov 4, 2015
#4
0

Yes you are right.

It is my experience that even very sophisticated calcs can't handle roots of negative numbers.

I think Alan went into more detail on this once before. Maybe he will comment later. :/

Nov 4, 2015