Finding All Complex Number Solutions
Find all complex number solutions for the equation \(z^4 = 16\).
Find the Roots of a Complex Number
Find all the roots of the complex number \(z = 8(cos(\frac{\pi}{3}) + i sin(\frac{\pi}{3}))\).
Complex Operations
$\frac{12 \operatorname{cis}\left(\frac{8}{3} \pi\right)}{11 \operatorname{cis}\left(\frac{12}{11} \pi\right)}$
Rationalizing with Complex Conjugates
Let \( z = 1 + i \sqrt{3} \). Compute \( \frac{z}{1 - z} \) and simplify the result.
Trigonometric Form of a Complex Number
$\frac{4 \operatorname{cis}\left(152^{\circ}\right)}{3 \operatorname{cis}\left(108^{\circ}\right)}$
Finding the Complex Conjugate
Find the complex conjugate of the complex number \(z = 3\cos\theta + 3i\sin\theta\) where \(\theta = \frac{\pi}{6}\).
Finding the Magnitude of a Complex Number
Find the magnitude of the complex number \(z = 3 \cos(\theta) + 3i \sin(\theta)\) where \(\theta = \frac{\pi}{4}\).