# Thread: Complex analysis, need bright light

1. ## Complex analysis, need bright light

Hello,

I'm not a mathematician but I'm trying to help a friend here struggled with this , this is naturally why I went to this forum:

If C is the semicircle $\left| z \right| =2$,Re(z)>0,prove that

Hopping that a good soul could help me.

2. Originally Posted by Izanagi
Hello,

I'm not a mathematician but I'm trying to help a friend here struggled with this , this is naturally why I went to this forum:

If C is the semicircle ,,prove that

Hopping that a good soul could help me.
What is the integration with respect to?? Be that as it may, start by noting that a general property of integrals is $\left| \int ( ) \right| \leq \int |( ) |$.

3. Thank you for your reply,

I've made mistake in the formula, I just edit it.

and i understand $\left| \int ( ) \right| \leq \int |( ) |$ but later what should we do for x^4+iy^4 ?

Would you have hint to solve this?

thanks again

4. Originally Posted by Izanagi
Thank you for your reply,

I've made mistake in the formula, I just edit it.

and i understand $\left| \int ( ) \right| \leq \int |( ) |$ but later what should we do for x^4+iy^4 ?

Would you have hint to solve this?

thanks again
On $C$, $|dz| = 4 \pi$ and $|x^4 + i y^4| = 8 |\cos^4 \theta + i \sin^4 \theta| \leq 8 |\cos \theta + i \sin \theta| = 8$.

5. Hello,

Thanks a lot for your help, that is brilliant. With your explanations my friend has been able to solve this.