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# Index problem [Solved!]

### My question

What is the difference between (-1)^2/2 and ((-1)^2)^1/2?

### Relevant page

2. Basic Operations in Complex Numbers

### What I've done so far

I tried expanding each out using complex number laws, but I'm not sure what I'm doing.

X

What is the difference between (-1)^2/2 and ((-1)^2)^1/2?
Relevant page

<a href="/complex-numbers/2-basic-operations.php">2. Basic Operations in Complex Numbers</a>

What I've done so far

I tried expanding each out using complex number laws, but I'm not sure what I'm doing.

## Re: Index problem

I'm not very clear what (-1)^2/2 means. (Please use the math input system - it makes it much easier for use to read your math.)

If we take the final 2 to mean "half of", then it probably means ((-1)^2)/2 = 1/2

The second expression, ((-1)^2)^1/2 if written ((-1)^2)^(1/2) means "the square root of (-1) squared".

In this case, (-1)^2 = 1 and the square root of 1 is 1.

Hope that helps.

X

I'm not very clear what (-1)^2/2 means. (Please use the math input system - it makes it much easier for use to read your math.)

If we take the final 2 to mean "half of", then it probably means ((-1)^2)/2 = 1/2

The second expression, ((-1)^2)^1/2 if written ((-1)^2)^(1/2) means "the square root of (-1) squared".

In this case, (-1)^2 = 1 and the square root of 1 is 1.

Hope that helps.

## Re: Index problem

Actually what i meant was,is {(-1)^(1/2)}^2 a real number?

X

I found your solution very helpful,well part of it.

Actually what i meant was,is {(-1)^(1/2)}^2 a real number?

## Re: Index problem

Hi again

Yes, it is a real number.

You have the equivalent of the square of the imaginary number, j. The answer is real, and it is -1.

1. Basic Definitions of Complex Numbers

X

Hi again

Yes, it is a real number.

You have the equivalent of the square of the imaginary number, j. The answer is real, and it is -1.

<a href="/complex-numbers/1-basic-definitions.php">1. Basic Definitions of Complex Numbers</a>

## Re: Index problem

Hi,it's me again.

What I think is that {(-1)^(1/2)}^2=sqrt(-1)^2,which is j^2=-1.

So I want to ask this,does it mean complex numbers are also REAL?

X

Hi,it's me again.

What I think is that {(-1)^(1/2)}^2=sqrt(-1)^2,which is j^2=-1.

So I want to ask this,does it mean complex numbers are also REAL?

## Re: Index problem

Hi again

Complex numbers consist of a real part and an imaginary part.

You can have the following and call them all complex.

3 + 5j
3 + 0j
0 + 5j

But really, the first is complex, the second is real, the 3rd is imaginary.

Good luck with it.

X

Hi again

Complex numbers consist of a real part and an imaginary part.

You can have the following and call them all complex.

3 + 5j
3 + 0j
0 + 5j

But really, the first is complex, the second is real, the 3rd is imaginary.

Good luck with it.