Let I= ∫_(∣z∣=π) ((tan(z^− ))/(z−4)) dz J=∫_(∣z∣=π) ((cos(z^− ))/(z−4)) dz and K=∫_(∣z∣=π) ((cos(Re(z))cos(Im(z)))/(z−4))dz Show that I=J(√2)=−iπ Show that J=K


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Question Number 134998 by snipers237 last updated on 09/Mar/21

$L e t I = \int_{∣ z ∣= π} \frac{t a n (\bar{z})}{z - 4} d z$ $J = \int_{∣ z ∣= π} \frac{c o s (\bar{z})}{z - 4} d z a n d K = \int_{∣ z ∣= π} \frac{c o s (R e (z)) c o s (I m (z))}{z - 4} d z$ $S h o w t h a t I = J \sqrt{2} = - i π$ $S h o w t h a t J = K$
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