# Complexity

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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: |