JEE Main 2022 · 28 Jun · Shift 1 · Mathematics Q29

MathematicsInteger+4 / -1Question 29 of 90

The number of elements in the set $\left\{z=a+ib\in\mathbb C:a,b\in\mathbb Z\text{ and }1<|z-3+2i|<4\right\}$ is ______.

Your answer

Answer and worked solution

Official answer: 40

Lattice points with $1<u^2+v^2<16$ , $u=a-3$ , $v=b+2$ .

Count $u^2+v^2\le15$ . $u=0$ : 7; $u=\pm1$ : 14; $u=\pm2$ : 14; $u=\pm3$ : 10. Total 45. Remove the 5 with $u^2+v^2\le1$ .

Answer: 40

JEE Main 2022 · 28 Jun · Shift 1, Mathematics question 29