Unformatted text preview: j cos z j ; j sin z j > 1 in the complex plane. 6. Express each of the following complex numbers in rectangular form. ( a ) sin & 1 2 ; ( b ) cos & 1 & i p 8 ± ; ( c ) cosh & 1 ( ± 1) ; ( d ) sinh & 1 & i= p 2 ± : Note that cos ( iu ) = cosh u ; sin ( iu ) = + i sinh u for any real number u . 7. Arfken & Weber Problem 6 : 1 : 15 . Find all the zeros of the functions ( a ) sin z ; ( b ) cos z ; ( c ) sinh z; ( c ) cosh z : Note that z = x + iy in rectangular form. 8. Arfken & Weber Problem 6 : 1 : 17 . In the quantum theory of photoionization, we encounter the identity ² ia ± 1 ia + 1 ³ ib = exp ´ ± 2 b cot & 1 a µ ; where a and b are real numbers. Verify this identity. 1...
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 Spring '09
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 Complex Numbers, Complex number, Arfken, Weber Problem

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