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Let-I-z-pi-tan-z-z-4-dz-J-z-pi-cos-z-z-4-dz-and-K-z-pi-cos-Re-z-cos-Im-z-z-4-dz-Show-that-I-J-2-ipi-Show-that-J-K-

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Question Number 134998 by snipers237 last updated on 09/Mar/21
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
LetI=∫∣z∣=πtan(z−)z−4dzJ=∫∣z∣=πcos(z−)z−4dzandK=∫∣z∣=πcos(Re(z))cos(Im(z))z−4dzShowthatI=J2=−iπShowthatJ=K

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