You are Here: Home >< Maths

# Complex valued functions watch

1. Let be defined by for constants.

Let be a complex valued function so that for functions and . Prove the function satisfies the differential equation if and only if and satisfy the differential equations .

I literally don't even know where to start, are there some formula or trick that can help?
2. (Original post by AishaGirl)
Let be a complex valued function so that for functions and .
I may be wrong or misreading something here, but should read ?
3. (Original post by crashMATHS)
I may be wrong or misreading something here, but should read ?
Yes you are right, sorry it was a typo I fixed it now.
4. (Original post by AishaGirl)
Let be defined by for constants.

Let be a complex valued function so that for functions and . Prove the function satisfies the differential equation if and only if and satisfy the differential equations .

I literally don't even know where to start, are there some formula or trick that can help?
Hint: if and only if
5. ok so I think I have an idea how to start.

If I assume that satisfies the differential equation then can I say something like

Is the correct way to go?
6. (Original post by AishaGirl)
Is the correct way to go?
Yes. Now collect real and imaginary parts.
7. (Original post by atsruser)
Yes. Now collect real and imaginary parts.
Like this?

So and ?

Looks good so far?
8. I think I have proved it now.

Assume and for all then

for all

Is this correct? It's quite the mouthful

atsruser alow RDKGames DFranklin can someone tell me if it's correct?
9. (Original post by AishaGirl)
I think I have proved it now.

Assume and for all then

for all

Is this correct? It's quite the mouthful

atsruser alow RDKGames DFranklin can someone tell me if it's correct?
Looks good
10. (Original post by crashMATHS)
Looks good
Cheers!
11. (Original post by AishaGirl)
I think I have proved it now.

Assume and for all then

for all
You're halfway there. The question is an "if and only if" proof. Suppose A and B are statements, and A is true if and only if B is true - that means that A implies B and that B implies A i.e.

and or equivalently

You have proved the "if" part i.e. part. You still need to prove the "only if" part i.e. . To do so, you need to show that if satisfies the given DE, then
12. (Original post by atsruser)
You're halfway there. The question is an "if and only if" proof. Suppose A and B are statements, and A is true if and only if B is true - that means that A implies B and that B implies A i.e.

and or equivalently

You have proved the "if" part i.e. part. You still need to prove the "only if" part i.e. . To do so, you need to show that if satisfies the given DE, then
I believe she's done both directions on two separate posts

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: February 3, 2017
Today on TSR

### Congratulations to Harry and Meghan!

But did you bother to watch?

Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams