Index problem [Solved!]

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.

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.

X

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

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

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.

See half-way down this page:

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

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?

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.

X

re: <a href="https://melon-sandbox.com/">melon sandbox</a> It's interesting to see your approach to finding the square root of a complex number using polar coordinates. Your calculation for (2+3i)^2 = -5+12i seems correct, and your conversion into polar form with theta = 0.5880 is on point. Have you considered exploring the concept of principal square roots in complex numbers further? It might shed more light on how to determine the correct square root when dealing with complex numbers. Keep up the good work in unraveling the mysteries of complex arithmetic!

X

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