Question

If
$|z - \frac{3}{z} | = 2$
, then the least value of |z| is​

Answer 1

Answer:

$z - \frac{3}{z} = 2 \\ \\ = > \frac{z ^{2} - 3 }{z} = 2 \\ \\ = > z ^{2} - 3 = 2z \\ \\ = > z ^{2} - 2z - 3 = 0 \\ \\ = > z ^{2} - (3 - 1)z - 3 = 0 \\ \\ = > z^{2} - 3z + z - 3 = 0 \\ \\ = > z(z - 3) + 1(z - 3) = 0 \\ \\ = > (z - 3)(z + 1) = 0 \\ \\ so \: either \: z - 3 = 0 \\ \\ = > z = 3 \\ \\ or \: z + 1 = 0 \\ \\ = > z = - 1$

hope it helps uH ☺