# Find the real part

1. Jun 1, 2014

### MissP.25_5

Hello, everyone.

Can some help me finish this solution? I am stuck. The questions is to find the real part of
i*sin(∏/4 + i).

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2. Jun 1, 2014

### LCKurtz

Use $e^{i\theta} = \cos \theta + i\sin\theta$ and its conjugate with $\theta = i$.

3. Jun 1, 2014

### MissP.25_5

Which part should I use that? I don't get it.

4. Jun 1, 2014

### LCKurtz

Solve the Euler equations for $e^{i\theta}$ and $e^{-i\theta}$ for the sine and cosine in terms of the exponentials. Surely your book has those formulas.

5. Jun 1, 2014

### MissP.25_5

Does that mean I didn't have to use the trig identity?

6. Jun 1, 2014

### LCKurtz

You just need $\sin i$ and $\cos i$ to finish, don't you? You can get them from the above formulas.

7. Jun 1, 2014

### MissP.25_5

Err...you mean like this? But it gets complicated.

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8. Jun 1, 2014

### MissP.25_5

Wait, I think I got it. Hold on, let me try and solve it and I will show it you.

9. Jun 1, 2014

### MissP.25_5

Is this correct?

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10. Jun 1, 2014

### LCKurtz

That looks correct. Notice that you could have substituted the exponentials for $\sin(\frac \pi 4 + i)$ directly, avoiding using the addition formulas.

11. Jun 1, 2014

### MissP.25_5

How to substitute the exponentials for $\sin(\frac \pi 4 + i)$ directly?

12. Jun 1, 2014

### LCKurtz

$\sin \theta = \frac {e^{i\theta}-e^{-i\theta}}{2i}$, the same formula you used before.

13. Jun 1, 2014

### MissP.25_5

You mean like this? But then how do I finish it? Looks complicated there.

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• ###### IMG_6388.jpg
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14. Jun 1, 2014

### SammyS

Staff Emeritus

What happened to $\ i\$ in the denominator?

Do you know what $\ e^{i\pi/4}\$ is ?

15. Jun 1, 2014

### MissP.25_5

I forgot to write the i.
$\ e^{i\pi/4}\ is equals to cos∏/4 + isin∏/4, right? And that makes it equals to 1/√2 + i/√2, right? 16. Jun 1, 2014 ### SammyS Staff Emeritus Yes, and$\ e^{-i\pi/4}= \ ? ##

17. Jun 1, 2014

### MissP.25_5

Thanks, I got it!!!!Yay! Thank you!

Last edited: Jun 2, 2014
18. Jun 2, 2014

### SammyS

Staff Emeritus
Good!!