Solving Complex Expressions: 1/z^2 & 1/z^3

[ENGR_student]

Hello I'm studying complex numbers for class and the question is stated as:
Let z=1+2i
Find:
a) 1/z^2
b) 1/z^3

I was thinking just to multiply by the conjugate (1-2i)^2 for (a) and similarly for (b).
Would that be correct in solving it?

 

[mfb]

You can do that, right.
Alternatively, calculate 1/z first, and then calculate powers of that.

As this looks like homework, I moved your thread.

 

[ENGR_student]

Oh thank you!
I apologize if I put it in the wrong thread!

 

[skiller]

Oh thank you!
I apologize if I put it in the wrong thread!

Firstly, let's establish what you are actually asking.

For example, the way you wrote it, 1/z^2 = $\frac{1}{z^2}$, NOT $(\frac{1}{z})^2$

EDIT: Please ignore. Complete brain-fart by me there!

 

[mfb]

For example, the way you wrote it, 1/z^2 = $\frac{1}{z^2}$, NOT $(\frac{1}{z})^2$

Where is the difference?

 

[skiller]

Where is the difference?

Thanks. I simply cannot believe what I wrote in my previous post.

I blame lack of sleep...:zzz:

 

[HallsofIvy]

Surely there must be some way to completely delete a post so that those of us who post a really stupid idea can pretend it never happened!?