Findinf residue of 1/5+4sin(deta)

[doey]

Homework Statement

it ask me to integral from 0 to 2pi for 1/[5+4sin(deta)]

Homework Equations

i knoe i nid to find out the pole bu convert sin(deta) into exponential fomat

The Attempt at a Solution

after i solve it until 2z^2+5iz-2 i stucked,can i juz use [-b+-squarot[b^2-4ac]]/2a formula to solve this by juz let my b=5i?
and i get the answer is in negative value,if i do that.i think i might wrong ,any one can help me?

 

[Dick]

Homework Statement

it ask me to integral from 0 to 2pi for 1/[5+4sin(deta)]

Homework Equations

i knoe i nid to find out the pole bu convert sin(deta) into exponential fomat

The Attempt at a Solution

after i solve it until 2z^2+5iz-2 i stucked,can i juz use [-b+-squarot[b^2-4ac]]/2a formula to solve this by juz let my b=5i?
and i get the answer is in negative value,if i do that.i think i might wrong ,any one can help me?

Yes. You can use the quadratic equation to solve something like that. But I don't think you've got the right quadratic and I don't know what "i get the answer is in negative value". You really need to show your work.

 

[doey]

Yes. You can use the quadratic equation to solve something like that. But I don't think you've got the right quadratic and I don't know what "i get the answer is in negative value". You really need to show your work.

∫1/5+4sin(deta) dθ =∫(dz/iz)/[5+4(z/2i-1/2iz)]
= ∫(dz)/[5iz+4(iz^2/2i-iz/2iz)]
= ∫(dz)/[5iz+(4iz^2)/(2i)-4iz/2iz)]
=∫(dz)/[5iz+2z^2-2]

then i nid solve 5iz+2z^2-2 to get my pole,am i wrong? then i will get my root in -0.5i and -2i.

 

[Dick]

∫1/5+4sin(deta) dθ =∫(dz/iz)/[5+4(z/2i-1/2iz)]
= ∫(dz)/[5iz+4(iz^2/2i-iz/2iz)]
= ∫(dz)/[5iz+(4iz^2)/(2i)-4iz/2iz)]
=∫(dz)/[5iz+2z^2-2]

then i nid solve 5iz+2z^2-2 to get my pole,am i wrong? then i will get my root in -0.5i and -2i.

Yep, that's what I get. I made a mistake but I caught it thanks you to showing what you did.