For z₁ = 5 - 2i and z₂ = -3 + 6i, find z₁ + z₂ and 2z₁ - z₂ in the form a + ib.

Add and take away part by part. Multiply out the brackets and put $-1$ for $i^2$: $(a + ib)(c + id) = (ac - bd) + i(ad + bc)$. The commutative, associative and distributive laws hold, and so do all the algebraic identities.