How many distinct complex roots does \(z^4=3-4i\) have?

What is the modulus of each solution of \(z^3=8\)?

Solve \(z^2=4\) over \(\mathbb C\).

Solve \(z^2=-4\).

Find the cube roots of \(8\) in exponential form.

Find all square roots of \(3+4i\).

Solve \(z^3=-1\) in exponential form.

Find the fourth roots of \(16\) in exponential form.

Solve \(z^3=1+i\) in polar form.

Solve \(z^2=2-2i\) in polar form.

Verify that \(2^{1/6}e^{3\pi i/4}\) is a solution of \(z^3=1+i\).

Explain why \(z^5=0\) has only one distinct root, not five distinct roots.

Find all \(z\) such that \(z^4=-16\).

Find all \(z\) such that \(z^3=-8i\).

For which positive real \(r\) do the roots of \(z^3=re^{i\pi/3}\) have modulus \(2\)?

For which integers \(k\) should be used to list the distinct roots of \(z^6=5e^{i\pi/7}\), and why?

Find all square roots of \(-3+4i\) in rectangular form.

A learner solves \(z^3=1+i\) using only \(\arg(1+i)=\pi/4\) and gives one root. Explain the missing step.

Prove that the roots of \(z^n=a\), with \(a\ne0\), are equally spaced in argument.

Show that if \(w\) is one solution of \(z^n=a\), then every solution is \(w\omega\), where \(\omega^n=1\).