Given a complex number $z$, determine its locus, given that $w=\frac{i}{z^{2}+1}$ belongs on the real axis (i.e. $w$ is a real number)
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Waiting till next week, for your ideas and thoughts.
Quadratics, polynomials, partial fractions, logarithms, binomial th., combinatorics, number theory, induction, arith.-geom. series, axioms of the reals, $2d$, $3d$ Coord. and vector geom., functions, trigonometry, sequences, convergence, limits, continuity, Differential and Integral Calculus, Complex numbers, vectors, groups, rings, fields, Statistics, Probability, series expansions and ratios of convergence, Differential Eq., arithmetic methods and approx., Euclidean geometry, logic, .... etc
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