[复变函数与积分变换].焦红伟&尹景本.文字版.PDF.pdf

1 正确 2 不正确 3 正确 4 正确 13

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(1) 正确; (2) 不正确; (3) 正确; (4) 正确 . 13 .用三角函数定义或用三角公式 . 14 (1) sh1 (2) 13 5 . 15 1 2 i 2 k π ,主值为 1 i 2 π 4 ln5 iarctan (2 1) i 3 k + + π ,主值为 4 ln5 ( arctan )i 3 + π − . 16 sin1ch1 icos1sh1 + 1 1 e e 2 + ie 2 e (cosln3 isinln3) k π + 1 2 4 ln 2 ln 2 e cos isin 2 2 k + π + . 17 k 为任意整数 . (1) ln 4 i (1 2 ) k + π + (2)i (3) ( ) iln 2 3 2 k ± + π (4)i k π (5) ln 2 i 2 3 k π + + π . 3 1 (1) 1 1 i 3 3 + (2) 1 5 i 2 6 + (3) 1 1 i 2 6 . 2 (1) 1 5 i 6 6 + (2) 1 5 i 6 6 + (3) 1 13 i 6 6 + . 3 π i 4 .不一定成立,例如, ( ) , 1 f z z z = = ,则
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