Homework1 - Physics 401 - Homework #1 1) (3 points) Complex...

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Physics 401 - Homework #1 1) (3 points) Complex numbers are commonly expressed in two forms: cartesian ( iy x z ) and polar ( ). Convert i Ae z i 1 1 to both of these forms, and state explicitly the values of x, y, A, and  2) For any complex number, 1 z z . a) (3 points) Show that this is true using the cartesian form ( iy x z ). b) (3 points) Show that this is true using the polar form ( ). i Ae z Which method is easier? 3) (1 point each, 4 points total) Prove the following identities for complex numbers: a) Re(z) = (z +z*)/2 b) Im(z) = (z - z*)/2i c) cos( ) = [exp(i ) + exp(-i )]/2 d) sin( ) = [exp(i ) - exp(-i )]/2i 4) (1 point each, 4 points total) a) What is the phase of the following wavefunction?: ) ( ) , ( t kx i Ae t x b) Show that the phase is shifted by /2 when the function is multiplied by i c) Show that the phase is shifted by when the function is multiplied by -1. d) Suppose we multiply the wavefunction by a phase factor
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Homework1 - Physics 401 - Homework #1 1) (3 points) Complex...

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