Algebra
De Moivre's Theorem
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 \(z = re^{i\theta}.\)
Given a complex number \(z = e^{ix}\), for which of the following values of \(x\) is the quantity \(\text{Re}(z)\text{Im(z)}\) minimized?