Residue at poles of complex function

[jaus tail]

Homework Statement

Homework Equations

First find poles and then use residue theorem.

The Attempt at a Solution

Book answer is A. But there's no way I'm getting A. The 81 in numerator doesn't cancel off.

 

[Dick]

Homework Statement

View attachment 219529

Homework Equations

First find poles and then use residue theorem.

The Attempt at a Solution

View attachment 219528
Book answer is A. But there's no way I'm getting A. The 81 in numerator doesn't cancel off.

Be careful. You don't multiply the function by $(3z+2)^3$ before you differentiate it. What's the correct factor? You won't get the books answer A in any case, but that's the books problem.

 

[FactChecker]

I don't get your answer or any of the answers above. It's hard for me to read your writing.

 

[jaus tail]

Be careful. You don't multiply the function by $(3z+2)^3$ before you differentiate it. What's the correct factor? You won't get the books answer A in any case, but that's the books problem.

The (3z+2)³ will get canceled when I find residue at z = -2/3, just like the (3z-2)³ part will get canceled when I find residue at z = 2/3.

 

[Dick]

The (3z+2)³ will get canceled when I find residue at z = -2/3, just like the (3z-2)³ part will get canceled when I find residue at z = 2/3.

The residue formula has $(z-a)^3$ where $a=(-2/3)$. That's not $(3z+2)^3$.

 

[jaus tail]

Yeah you're right. In solved example they've broken 0.5z - 1.5i to z - 3j and multiplied 2 into numerator. Thanks.