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Unformatted text preview: i i and they are all real. ( Hint : Remember the denition of the complex exponential: w z = exp( z ln w ).) 5. Prove Eulers identity e i = cos + i sin as follows: show that both sides of the identity satisfy the same rst order dierential equation, and they are equal for = 0. 6. Prove the trigonometric identities for cos( a + b ) and sin( a + b ) by taking the real and imaginary parts of the identity exp( i ( a + b )) = exp( ia )exp( ib ). You may of course use the fact that exp( i ) = cos + i sin ....
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This note was uploaded on 12/29/2011 for the course PHYSICS 374 taught by Professor Jacobson during the Fall '10 term at Maryland.
- Fall '10