Understanding Im(z)^2: Clarifying the Calculation in Your Textbook

[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) ?

 

[Ray Vickson]

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) ?

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?

 

[johann1301]

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?

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?

 

[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...

 

[Fredrik]

$\operatorname{Im}(z)^2$ 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 $z^2$.