Find \\(|3+4i|\\).

Find \\(|-5+0i|\\).

Find \\(|0-7i|\\).

Find \\(|1+i|\\).

Find \\(|-6+8i|\\).

Find \\(|2-3i|^2\\).

Find the distance from the origin to the point represented by \\(-12+5i\\).

If \\(z=2e^{i\theta}\\), what is \\(|z|\\)?

Find \\(|(1+2i)(3-4i)|\\) using multiplication first.

Find \\(\\left|\frac{3+4i}{1-2i}\right|\\).

Verify \\(|z|^2=zz^*\\) for \\(z=2-5i\\).

Explain geometrically why \\(|a+bi|\\) cannot be negative.

Find real \\(t\\) if \\(|t+3i|=5\\).

Find \\(t\\ge0\\) if \\(|(t-1)+2i|=\\sqrt{13}\\).

For which real \\(t\\) does \\(|t+(t-2)i|=2\\)?

For which real \\(t\\) is \\(|(t+i)^2|=10\\)?

Find all real \\(t\\) such that \\(|t+2i|=|3-ti|\\).

A learner says \\(|3-4i|=3-4i\\). Diagnose the error and correct it.

Prove that \\(|a+bi|=0\\) implies \\(a+bi=0\\).

Explain why \\(|z|=|z^*|\\) for every complex number \\(z\\).