# Complexity

The questions below are due on Monday March 01, 2021; 10:00:00 PM.

You are not logged in.

Note that this link will take you to an external site (https://shimmer.csail.mit.edu) to authenticate, and then you will be redirected back to this page.
Note that this exercise is intended to be solved by hand, without the use of computation.

Determine the real and imaginary parts of each of the following expressions. Enter your answer as a Python expression, which can depend on pi, e, and/or sqrt. The questions in this part will be graded automatically.

3e^{j\pi/3} + 4e^{-j\pi/6}

 Real Part: Imaginary Part:

\left( \sqrt{3} + j\right)^{11}

 Real Part: Imaginary Part:

\sqrt{-j}

 Real Part: Imaginary Part:

\left(\sqrt{2}e^{j\pi/2} + \sqrt{2}e^{j\pi/4} + \frac{2}{\sqrt{2}}e^{j5\pi/4} + \frac{1}{\sqrt{2}}e^{j\pi} - \frac{1}{\sqrt{2}}j \right)^{218}

 Real Part: Imaginary Part: