Add \\((2+3i)+(5+i)\\).

Add \\((-4+6i)+(4-6i)\\).

Find \\((7-2i)+(-3+9i)\\).

Find \\((-8-i)+(2+5i)\\).

Add \\((3+4i)+(1-7i)+(6+2i)\\).

Simplify \\((5-3i)+(2+i)-(4-6i)\\).

What complex number must be added to \\(6-5i\\) to get \\(10+2i\\)?

Two displacement vectors are represented by \\(3+2i\\) and \\(-1+5i\\). Find the combined displacement.

Find \\(z+w\\) if \\(z=-2+11i\\) and \\(w=9-4i\\).

Find \\(z\\) if \\(z+(4-3i)=-2+8i\\).

Show with \\(z=2-5i\\) and \\(w=-7+i\\) that \\(z+w=w+z\\).

Explain why adding \\(0+0i\\) leaves \\(a+bi\\) unchanged.

Find \\(p\\) and \\(q\\) if \\((p+2i)+(3+qi)=8-5i\\).

Find \\(a\\) and \\(b\\) if \\((a+bi)+(a-bi)=14\\).

For which real \\(t\\) is \\((t+2i)+(3+(t-5)i)\\) purely real?

For which real \\(t\\) is \\((t^2+i)+(4+(t-1)i)\\) equal to \\(8+0i\\)?

Find all real \\(t\\) such that \\((t+1)+(2t)i\\) added to \\((3-t)+(t^2-4)i\\) is real.

A learner adds \\((2+3i)+(4+5i)\\) and gets \\(6+15i\\). Diagnose the mistake and correct it.

Prove that the additive inverse of \\(a+bi\\) is \\(-a-bi\\).

Explain why complex addition corresponds to vector addition in the complex plane.