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# De Moivre's Theorem

De Moivre's Theorem shows that to raise a complex number to the nth power, the absolute value is raised to the nth power and the argument is multiplied by n.

Which of the following is equivalent to the conjugate of the complex number \(4e^{i\pi /4}?\)

The complex number \(z = -4 + 3i\) can be converted into the polar form \(z = re^{i\theta}.\)

What is the value of \(r?\)

If \(z = \sqrt{3} + i\), then what is the value of \(z^6?\)

Hint: You might want to start by converting \(\sqrt{3} + i\) into the form \(z = re^{i\theta}.\)

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