# Homework Help: Complex exponentials - homework

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1. Feb 12, 2017

### Poetria

• Thread moved from the technical Math forums, so no Homework Template is shown
Could you give me a hint how to attack this problem?

Find a complex number z = a+i*b such that f(t)=Re e^(z*t) where f(t)=cos(2*pi*t)

I have begun as follows:

e^((a+i*b)*t)=e^(a*t)*(cos(b)+i*sin(b))

Re e^(z*t)= e^(a*t)*cos(b)

What to do now?

2. Feb 12, 2017

### Ssnow

Hi, $t$ is real? If is yes so you must find $a,b$ from $e^{at}\cos{b}=cos(2\pi t)$ ...

3. Feb 12, 2017

### Poetria

Yes, t is a real variable.I know I must but how? Thank you very much. :)

4. Feb 12, 2017

### Ssnow

another hint: $e^{at}cos{(b)}=e^{0t}cos{(2\pi t)}$, you can read now $a=...$ and $b=...$

5. Feb 12, 2017

### Poetria

Ok, I got it. :) Great. Thank you very much. :)