Solve \((3+i)z=0\).

State the condition on \(a\) for \(az+b=0\) to have a unique complex solution.

Solve \(2z+6=0\) over \(\mathbb C\).

Solve \(iz+4=0\).

Solve \((1+i)z=2\) and give the answer in standard form.

Solve \((2-i)z=5+i\).

Solve \((3-2i)z+(4+i)=0\).

Solve \((1-3i)z=2+5i\).

Solve \((2+i)z-(3-4i)=1+i\).

Solve \((1+i)z+2\overline{(1-i)}=0\), treating \(z\) as the only unknown.

Find \(z\) if \((4+i)z=7-2i\), then verify by substitution.

Classify the solutions of \(0z+(3-i)=0\).

Find all complex \(z\) satisfying \((1+i)z+(2-i)=3z\).

Solve \(\dfrac{z}{1+i}+\dfrac{z}{1-i}=4\).

For which complex numbers \(b\) does \((2-i)z+b=0\) have the solution \(z=1+2i\)?

For which real values of \(t\) does \((t+i)z=1\) have a unique complex solution?

Find all real \(t\) for which \((t-2i)z=t^2-4\) has solution \(z=0\).

A learner solves \((1-i)z=2\) and writes \(z=1+i\). Diagnose the answer by substitution and correct it if necessary.

Explain why the equation \((a+bi)z+c=0\) can fail to have a unique solution, where \(a,b,c\in\mathbb R\).

Show that \((1+2i)z+(3-i)=0\) has exactly one solution and find it.