The number of elements in the set z = a + ib ∈ ℂ: a, b ∈ ℤ and 1 <...

We know that $\left|z - \left(3 - 2i\right)\right| = r$ represents a circle with centre \left(3, - 2\right)$and radius$r$.</p><p><img src="https://cdn-question-pool.Quantrex.app/pyq/jee_main/d18ef026-ba0d-49d6-9f8e-a0a7c28f3b49-image.png" style="width: 160px; height: 152px;" /></p><p>$1 < \left|z - 3 + 2i\right| < 4$</p><p>$1 < {\left(a - 3\right)}^{2} + {\left(b + 2\right)}^{2} < 16$</p><p>The ordered pairs of \left(a, b\right)$ satisfying the above inequality are \left(0, \pm 2\right), \left(\pm 2, 0\right), \left(\pm 1, \pm 2\right), \left(\pm 2, \pm 1\right)

\left(\pm 2, \pm 3\right), \left(3 \pm , \pm 2\right)$, \left(\pm 1, \pm 1\right)$, \left(2 \pm , \pm 2\right)$</p><p>\left(\pm 3, 0\right)$, \left(0, \pm 3\right)$, \left(\pm 3 \pm 1\right), \left(\pm 1, \pm 3\right)</p><p>i.e. total$40$elements are present in the given set</p>$