Find \\(\\operatorname{Re}(8-3i)\\).

Find \\(\\operatorname{Re}(-4+11i)\\).

Find \\(\\operatorname{Re}(6i)\\).

Find \\(\\operatorname{Re}(9)\\), treating \\(9\\) as a complex number.

Find \\(\\operatorname{Re}((2+3i)+(5-7i))\\).

Find \\(\\operatorname{Re}((1+i)(4-2i))\\).

Find \\(\\operatorname{Re}(5(2-9i))\\).

Find \\(\\operatorname{Re}(3e^{i\\pi})\\) using \\(\\operatorname{Re}(re^{i\theta})=r\\cos\theta\\).

Find \\(\\operatorname{Re}(z+w)\\) if \\(z=7-2i\\) and \\(w=-10+5i\\).

Find \\(\\operatorname{Re}\\left(\frac{1}{1-i}\right)\\).

Verify \\(\\operatorname{Re}(z)=\frac{z+z^*}{2}\\) for \\(z=-6+5i\\).

Explain why \\(\\operatorname{Re}(z+w)=\\operatorname{Re}(z)+\\operatorname{Re}(w)\\).

Find real \\(t\\) if \\(\\operatorname{Re}((t+2)+(3t-1)i)=9\\).

Find \\(t\\) if \\(\\operatorname{Re}((t+i)(2-i))=5\\).

For which real \\(t\\) is \\(\\operatorname{Re}((t+2i)^2)=0\\)?

For which real \\(t\\) does \\(\\operatorname{Re}\\left(\frac{t+i}{1+i}\right)=2\\)?

Find all real \\(t\\) such that \\(\\operatorname{Re}((t+i)(t-3i))=10\\).

A learner says \\(\\operatorname{Re}(2+5i)=2+5i\\). Diagnose the error.

Prove that \\(\\operatorname{Re}(cz)=c\\operatorname{Re}(z)\\) for real \\(c\\).

Give a counterexample to \\(\\operatorname{Re}(z_1z_2)=\\operatorname{Re}(z_1)\\operatorname{Re}(z_2)\\).