4.2.4—Straight lines

To find where a line meets a locus, parameterise the line, substitute its coordinates into the modulus or argument condition, and solve for permitted parameter values.

Check the parameter interval and retain only points satisfying every original condition. A quadratic parameter may represent two, one or no intersections.

Substituting z=1+iλ into |z|=√2 gives 1+λ²=2, so λ=±1 and two points on the circle.

Solving the squared modulus equation can introduce a sign or domain issue; verify in the unsquared condition.