- #1
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Homework Statement
Estimate ∫γ dz/(1 + z^4) as R→∞.
Note that letting z = Re^(it) for t in [0, π]:
|∫γ dz/(1 + z^4)|
= |∫(t = 0 to π) (iRe^(it) dt) / (1 + R^4 e^(4it))|
≤ ∫(t = 0 to π) R dt / |1 + R^4 e^(4it)|
≤ ∫(t = 0 to π) R dt / (R^4 - 1), since R > 1
≤ πR / (R^4 - 1).
but why does iRexp(it)=R ?
why does i exp(it)=1?
please help