Complex Analysis: Theory and Applications · Problem 5.4.6

Complex Integration — Howell & Matthews

Mathematics — Complex Analysis · complex-trig-evaluation

Problem

Express the following quantities in u+ivu + iv form. (a) cos⁡(1+i)\cos(1 + i). (b) sin⁡(π+4i4)\sin\left(\dfrac{\pi + 4i}{4}\right). (c) sin⁡2i\sin 2i. (d) cos⁡(−2+i)\cos(-2 + i). (e) tan⁡(π+2i4)\tan\left(\dfrac{\pi + 2i}{4}\right). (f) tan⁡(π+i2)\tan\left(\dfrac{\pi + i}{2}\right). (g) sinh⁡(1+iπ)\sinh(1 + i\pi). (h) cosh⁡iπ2\cosh \dfrac{i\pi}{2}. (i) cosh⁡(4−iπ4)\cosh\left(\dfrac{4 - i\pi}{4}\right).

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