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Picture complex numbers as points, find their modulus and conjugate and what they mean on the plane, then solve quadratic equations with a negative discriminant and find square roots of complex numbers.
Spot a quadratic equation, write a word problem as one, and solve it by splitting the middle term. Then check each root, and decide which roots make sense for the problem.
Complete the square, and turn it into the quadratic formula that solves every quadratic equation. Then read the discriminant to know, before solving, whether there are two roots, one or none.
Harder problems for the keen: equations that turn into quadratics, the sum and the product of the roots, and the greatest or least value of a quadratic, each with worked solutions and a timed paper.