.. title: Quantum Homework 1, Mon 2022-08-29
.. slug: homework01
.. date: 2022-08-29
.. tags: homework
.. category:
.. link:
.. description:
.. type: text
.. has_math: true
Due 2022-09-01 4pm in gradescope.
#. (5 points) Compute (5+2i)/(3+4i).
#. (5 pts) Compute the eigenvalues of $\\begin{vmatrix} 5&2\\\\3&4 \\end{vmatrix}$.
#. (5 pts) Considering complex numbers as points in the 2D plane, what is the geometric effect of multiplying a complex number by (.6-.8i) ?
#. (5 pts) Let c = 1 + i. Convert it to polar coordinates, calculate its fifth power, and revert the answers to Cartesian coordinates.
#. (5 pts) Find all the cube roots of c = 1 - i.
#. (5 pts) Invert the Hadamard matrix $\\frac{1}{\\sqrt{2}} \\begin{vmatrix} 1&1\\\\1&-1\\end{vmatrix}$.
Total: 30