# What does Im(z)^2

1. Aug 24, 2014

### johann1301

Just wondering what my textbook wants me to do with:

Im(z)2

Im i supposed to find the square of the imaginary part of z, or the imaginary part of z2?

Does Im(z)2 equal (Im(z))2 or Im(z2) ?

2. Aug 24, 2014

### Ray Vickson

I woulds guess that the imaginary part of $z^2$ would be written as $\text{Im}(z^2)$, so I would guess that you are being asked for $(\text{Im}(z))^2$. However, when in doubt, why not give both interpretations and both answers?

3. Aug 24, 2014

### johann1301

Yez, that would be the right way to go! I guess i was wondering if there were any strict rules. Also, perhaps it could be expressed in a similar manner as (sin(x))2, that is - most of the time - written as sin2x. Perhaps there is a standard for Im2(z) as well?

4. Aug 24, 2014

### BvU

I am inclined to think a book would want Im(z2), for a simple reason: finding Im(z) and then squaring it isn't much of an exercise. Finding the imaginary part of z2 is a bit more serious.
However, this is just an opinion. I'd have to flip through the book to see if the writer is that sloppy in more places....

5. Aug 24, 2014

### Fredrik

Staff Emeritus
$\operatorname{Im}(z)^2$ is a really weird notation. I would use $(\operatorname{Im} z)^2$ for the square of the imaginary part of z, and $\operatorname{Im}z^2$ for the imaginary part of $z^2$.