# Quantum Homework 1, Mon 2022-08-29

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