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.

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.

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.
See half-way down this page:
<a href="/complex-numbers/1-basic-definitions.php">1. Basic Definitions of Complex Numbers</a>

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?

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.